58 GS11 Abstracts

IP1

Multiscale Model Reduction Techniques for Flowsin High-contrast Heterogeneous Media and Appli-cations

The development of numerical algorithms for simulationsof flow processes in large-scale highly heterogeneous porousformations is challenging because properties of natural ge-ologic porous formations (e.g., permeability) display highvariability and complex spatial correlation structures whichcan span a hierarchy of length scales. It is usually necessaryto resolve a wide range of length and time scales, which canbe prohibitively expensive, in order to obtain accurate pre-dictions of the flow, mechanical deformation, and transportprocesses under investigation. In practice, some types ofcoarsening (or upscaling) of the detailed model are usuallyperformed before the model can be used to simulate com-plex processes. Many approaches have been developed andapplied successfully when a scale separation adequately de-scribes the spatial variability of the subsurface properties(e.g., permeability) that have bounded variations. Thequality of these approaches deteriorates for complex het-erogeneities without scale separation and high contrast. Inthis talk, I will describe multiscale model reduction tech-niques that can be used to systematically reduce the de-grees of freedoms of fine-scale simulations and discuss ap-plications to preconditioners. Numerical results will bepresented that show that one can improve the accuracyof multiscale methods by systematically adding new coarsebasis functions and obtain contrast-independent precondi-tioners for complex heterogeneities.

Yalchin EfendievDept of MathematicsTexas A&M Universityefendiev@math.tamu.edu

IP2

The Role of Applied Computational Mathematicsin the end-to-end Near-field Tsunami Early Warn-ing System in Indonesia

In the aftermath of the 2004 Indian Ocean Tsunami, theGerman Federal Government funded the development of anew near-field tsunami early warning system (GITEWS)for Indonesia as a multi-national multi-institutional sci-entific collaboration. The system is in operation sinceNovember 2008 and is being handed over to the IndonesianGovernment in the days of the SIAM Geosciences Meeting.Several tsunami events have occurred since the inaugura-tion of the system and have demonstrated the performanceof this highly sophisticated and integrated tool for mitigat-ing the effects of natural disaster. In the core of the system,several mathematical and computational techniques andprocedures play a key role to interpret earth observationdata and to make use of the information gained. Simulat-ing the specific components of the earth system is just thestart of the chain of mathematical processes involved. Arigorous (but simple and robust) uncertainty propagationand reduction model helps in determining the potential im-pact of a rupture. Statistical methods are used to develophazard maps and define risk zones. The presentation willgive an overview of the diverse technical components andsocietal considerations involved in the GITEWS TsunamiEarly Warning System. An emphasis will be laid on thecomputational mathematics aspects and their core role insolving the problem of near-field tsunami detection andearly warning. From this development, and the constraintsof real-time robust operational service, several conclusionscan be drawn for a more general geo-scientific computa-

tional perspective.

Jorn BehrensKlimaCampusUniversity Hamburgjoern.behrens@zmaw.de

IP3

Recent Advances in Full Waveform Global SeismicTomography of the Earth’s Mantle

Over the last 20 years, several generations of global tomo-graphic models of the earth’s mantle elastic structure havebeen developed, relying on simple theoretical approxima-tions to the 3D wavefield (i.e. ray theory and first ordernormal mode perturbation theory). Now, it is possible tocompute accurate synthetics in spherical geometry for ar-bitrary 3D structures using numerical approaches, such asthe Spectral Element Method, which is particularly wellsuited for global waveform tomography. The challenge hasbeen shifted from theoretical limitations to the length ofcomputations involved. I will discuss and illustrate currentsteps towards the development of next generation, high res-olution whole mantle models.

Barbara RomanowiczUniversity of California, Berkeleybarbara@seismo.berkeley.edu

IP4

Computational Challenges in Applications of Cou-pled Reservoir Geomechanics

Recent years have seen dramatic increase in the applicationof coupled hydro-thermo-mechanical numerical solutions topetroleum industry. In this context they are often referredto as Coupled Reservoir Geomechanics, and involve cou-pled solution of multiphase, thermal flow in porous me-dia, stress and deformation, and fracture mechanics. Thisgrowing discipline encompasses diverse problems such aswellbore stability, sand production, hydraulic fracturing,compaction and subsidence, fault reactivation etc. Suchapplications invariably involve large, complex fields andthey pose serious computational challenges. This talk willdiscuss some of them, including: Current state of the iter-ative strategies for the flow and stress coupling Grid con-struction, grid repair and generation of the geomechani-cal grid from the flow grid Creation and upscaling of thegeomechanical characterization and dealing with complexmedia (such as naturally fractured reservoirs) Scale issuesand dealing with local accuracy requirements All of thesetopics will be illustrated by examples of actual studies fromstudies of petroleum reservoirs and CO2 sequestration inaquifers.

Antonin SettariUniversity of CalgaryTaurus Reservoir SolutionsAsettari@taurusrs.com

IP5

3-D Finite-element Simulation of Transient Elec-tromagnetics in Complex Earth Media

The diffusion of low frequency EM fields in conductivemedia is the basis for controlled-source electromagnetic(CSEM) remote sensing of Earths subsurface. Over thepast decade, there have been many numerical approachesdeveloped for simulating CSEM in complex geological

GS11 Abstracts 59

media, including direct implementation of the coupledMaxwells equations, the popular double-curl electric fieldformulation, and the coupled vector and scalar potentialsformulation derived under the Coulomb gauge condition.In this talk, we present a new formulation that uses avariation of the Lorenz gauge that is well suited to finite-element (FE) modeling. Our formulation decouples thevector and scalar potentials into a separate diffusion equa-tion for the vector potential and Poissons equation for thescalar potential. It reduces the larger FE system that re-sults from the Coulomb gauge into two smaller decoupledsystems of FE equations. Moreover, this Lorenzian-gaugeformulation retains the advantages of both the double-curlelectric field and the Coulomb-gauge approaches; the re-sulting FE system not only has the minimum number ofunknowns but also can be used in the static limit usingan iterative solver. We illustrate the method for large 3-Dgeophysical CSEM problems and compare results with thefinite-element double-curl electric field approach and thefinite-difference Maxwell equation approach.

Jerry M. HarrisStanford Universityjerry.harris@stanford.edu

IP6

Atmospheric Convection in Weather and ClimateSimulations

Convection in the atmosphere, whether driven by heat-ing of the earth’s surface or by condensational heating inclouds, is one of the most difficult processes to representin our climate and weather models, and representing theseprocesses is critical given the large uncertainty associatedwith clouds in climate assessments and weather prediction.Convective updrafts are not resolved in climate model sim-ulations that use horizontal mesh spacings of 0(100 km),and they are severely under-resolved in weather predictionwhere the smallest horizontal mesh spacings are O(1 km).The issues associated with representing convection havesignificant implications for the design of the Navier-Stokessolvers used atmospheric models. In this talk I will brieflyoutline and provide examples of these issues and and dis-cuss their implications.

William C. SkamarockNational Center for Atmospheric Researchskamaroc@ucar.edu

CP1

Traveltime Computation and Two-Point SeismicRay-Tracing in Complex Velocity Models.

The problem of tracing seismic ray between two givenpoints plays a central role in many implementations, for ex-ample in tomographic velocity analysis. Traditional waysof two-point ray-tracing, such as shooting or ray bend-ing methods appear to be unstable and computationalexpensive in complex velocity anisotropic 3D models. Anew approach based on eikonal finite-difference solversis proposed. Numerical experiments using high-contrastisotropic and transversal isotropic models demonstrate theaccuracy of proposed two-point ray-tracing algorithms.

Serdyukov AleksanderINGG Russiaaleksanderserdyukov@yandex.ru

CP1

Seismic Velocity Modeling Using Genetic Algo-rithms, Binary Versus Real Valued Searches

From a statistical view seismograms are interpreted as ran-dom variables. The random component can be attributedto sources such as distant-dependent measurement error,human error in picking arrival phases, and random noiseattributed to travel path. Stochastic modeling of such phe-nomenon quantifies these random processes. Genetic algo-rithms are iterative stochastic models that evaluate pro-gressively improved mathematical models. We explore thebenefits of using binary versus real valued based geneticalgorithms in modeling seismic velocity structures.

K B. BoomerBucknell Universitykb.boomer@bucknell.edu

Richard A. BrazierThe Pennsylvania State University Dubois CampusCommonwealth College (Math Division)rab27@psu.edu

CP1

Appropriate Formulation of the Objective Functionfor a Better Integration of 4D Seismic Data to Con-strain Reservoir Models.

Calibrating reservoir models to flow data involves historymatching processes. Model parameters are iteratively ad-justed to minimize the misfit between the real data and thecorresponding simulated responses. The current formula-tion used to quantify the seismic data mismatch is neitherrepresentative of the difference between two images, nor ofmatching quality. We describe an alternative formulation,using methods rooted in image processing, to extract rel-evant information from seismic images and compute theirdissimilarity.

Ratiba DerfoulIFP Energies nouvellesLaboratoire de Mathematiques de l’INSA, INSA Rouenratiba.derfoul@ifpenergiesnouvelles.fr

Sebastien Da Veiga, Elodie TillierIFP Energies nouvellessebastien.da-veiga@ifpenergiesnouvelles.fr,Elodie.Tillier@ifpenergiesnouvelles.fr

Christian GoutINSA RouenLab. de Mathematiques de l’INSAchristian.gout@insa-rouen.fr

CP1

On the Stability of the Perfectly Matched Layer inTime-Dependent Elastic Wave Guides.

There are many wave propagation problems where bound-ary phenomenon such as surface or glancing waves are dom-inant. Typical examples are in seismology and earthquakeengineering, which can be described by the elastic waveequation in a waveguide. It has also been reported thatwhen an elastic waveguide is accompanied by free-surface(vanishing stresses) boundary conditions or clamped (van-ishing displacements) boundary conditions, the PML be-comes unstable and can not be used to truncate the com-putational domain. This is in part due to the existence

60 GS11 Abstracts

of backward propagating modes supported by the bound-ary conditions. In this talk we will discuss how to avoidthis instability. Analysis and numerical experiments willbe presented highlighting the practicality of our technique.

Kenneth Duru, Gunilla KreissDivision of Scientific ComputingUppsala Universitykenneth.duru@it.uu.se, gunilla.kreiss@it.uu.se

CP1

Identification of Multiple Layers in Geophysics Us-ing Optimization and Level Set Methods

A shape reconstruction method for geophysical objects bytemperature or hydraulic head measurements is presentedwhich uses adjoint equations and a level set function ap-proach. Temperature is measured on subdomains, e.g. rep-resenting boreholes. This information is used to recon-struct the shape of the geophysical layers. For this pur-pose shape optimization techniques are applied. Syntheticexamples demonstrate the use of the inverse method andits behavior in different configurations.

Michael HertyRWTH Aachen UniverstiyDepartment of Mathematicsherty@mathc.rwth-aachen.de

CP1

Estimation of Transmission Eigenvalues and the In-dex of Refraction Using Cauchy Data

Transmission eigenvalues have import applications in in-verse scattering theory. We show that transmission eigen-values can be computed from the near field Cauchy data.In addition, we apply an optimization method to estimatethe index of refraction based on the lowest transmissioneigenvalues. The numerical results validate the effective-ness of the method.

Jiguang SunDepartment of Mathematics, Delaware State Universitysunjiguang@yahoo.com

CP2

Spectral Methods on Semi-Infinite Domains for Im-plementation of Open Boundary Conditions

We adopt a spectral approach to open boundary conditions[Givoli, 2008] using Generalized Laguerre functions [Wanget al. 2009], discretizing the equations in a semi-infinitedomain attached to a finite region of interest. We consider1D Shallow Water Equations, with a spectral collocationin space, semi-implicit semi-Lagrangian discretization intime. Coupling with different finite-domain discretizationsshows that a reasonable number of base functions is suf-ficient to reach accuracy and efficiency without spuriousreflections at infinity.

Tommaso BenacchioFachbereich Mathematik und Informatik, FreieUniversitatBerlin, Germanybenacchio@math.fu-berlin.de

CP2

Elastic Effect on the Stability of Viscoelastic ShearFlows in the Limit of Infnite Weissenberg andReynolds Numbers

This work is concerned with the linear stability of viscoelas-tic shear flows of an Upper Convected Maxwell fluid underthe effect of elasticity. We are focused on the stability prob-lem of a few classes of simple parallel flows in the limit of in-finite Weissenberg and Reynolds numbers. We will discussthe numerical stability results. We consider plane Couetteand Poiseuille flow, the hyperbolic tangent shearlayer andthe Bickley jet flows. For all these flows, we shall considerfree surface boundary conditions as well as wall boundaryconditions. In the inviscid case, all the flows are unsta-ble for free surfaces. For wall bounded flows, the Couetteand Poiseuille flows are stable, while stability of the shearlayer and Bickley jet depends on the ratio of the channelwidth to the characteristic length scale of the profile. In allcases, we find that elasticity stabilizes and ultimately sup-presses the instability. Our numerical approach is basedon the spectral Chebyshev collocation method. We shallalso show that some flows, such as plane Poiseuille flowbetween two parallel free surfaces, also have short wave in-stabilities. This is in marked contrast to the wall boundedcase. In this case, no smooth velocity profiles unstablesto short waves are known, and for certain classes of flowsthere are even results ruling out short wave instability

Ahmed Kaffelvirginia techkaffel07@gmail.com

CP2

A Computational Framework for Ocean and Atmo-sphere Modeling Based on Parallel Adaptive FEMfor Unstructured Meshes

We present a computational framework based on paral-lel adaptive FEM for atmosphere and ocean simulationsas part of the Unicorn project. In order to achieve effi-cient representation of spatial scales we use adaptive meshrefinement. The framework can utilize massively parallelarchitectures to achieve the required model resolutions. Inour framework we treat the ocean/atmosphere as a turbu-lent incompressible fluid with variable density. We presentresults on the ongoing work.

Kaspar MullerSchool of Computer Science and ComunicationRoyal Institute of Technology KTHkasparm@kth.se

Johan Hoffman, Johan JanssonSchool of Computer Science and CommunicationRoyal Institute of Technology KTHjhoffman@nada.kth.se, jjan@nada.kth.se

CP2

Characteristics-Based Methods for AtmosphericSimulation on Modern Hardware

Immense distributed memory parallelism requires priori-tizing the lowering of communication burden in numeri-cal methods. Focusing on atmospheric simulation, I pro-pose herein various characteristics-based (CB) integrationmethods. With fully discrete explicit time stepping, CBmethods reduce communication and synchronization whileallowing large-CFL time steps. I will discuss the theory,

GS11 Abstracts 61

large-CFL accuracy, handling of source terms and multi-dimensionality, limiting of oscillations, and efficiency onaccelerator-based computing architectures.

Matthew NormanNorth Carolina State UniversityRaleigh, NCmatthew.ross.norman@gmail.com

CP2

Under-Resolved Les of Rayleigh-Benard Convec-tion; Effects of Prandtl Number Anisotropy

In [Piotrowski et al., JCP 228, 2009] the effects werediscussed of anisotropic numerical filtering in under-resolved large-eddy simulation (LES) on the organizationof Rayleigh-Benard convection at a finite Prandtl number.This study extends the linear stability theory of that ear-lier work to anisotropic Prandtl numbers, to asses the roleof disparate approximations to the governing equations inlarge-scale atmospheric codes. Asymptotic predictions ofthe linear theory are discussed and illustrated with com-putational examples.

Zbigniew P. PiotrowskiNational Center for Atmospheric Researchpiotrows@ucar.edu

Piotr SmolarkiewiczNCARMMMsmolar@ucar.edu

CP2

Finding Normal Modes of Semi-Enclosed Bays Us-ing the Statistical Modes of a Data Set of ModeledTsunami Wavefields

Understanding the resonant modes of bays and harboursis important for tsunami hazard assessment and moni-toring. Previous methods for determining normal modeshave adapted techniques developed for enclosed basins;but these generally rely on ad-hoc assumptions about theboundary between basin and ocean. We demonstrate amethod for identifying the normal modes using EmpiricalOrthogonal Function (EOF) analysis of modeled tsunamiwavefields which does not have this limitation, and showexamples for Poverty Bay and Monterey Bay.

William L. PowerGNS Sciencew.power@gns.cri.nz

Elena TolkovaJISAO / NOAA Center for tsunami researchelena.tolkova@noaa.gov

CP3

A Joint Inversion Scheme for Contaminant SourceZone Reconstruction

A parametric level set (PaLS) method is used to charac-terize contaminant source zone geometry and entrappedsaturation distribution from electrical resistance and hy-drological (downstream concentration) data. The low or-der representation provided by the PaLS approach allowsfor tractable computation of all sensitivities based on exactphysical models for resistance tomography and multiphase

flow and transport and yields a geometric inversion schemerequiring no explicit regularization still capable of resolvinghighly detailed structure.

Alireza Aghasi, Eric Miller, Andrew Ramsburg, LindaAbriolaTufts Universityalireza.aghasi@tufts.edu, elmiller@ece.tufts.edu,andrew.ramsburg@tufts.edu, linda.abriola@tufts.edu

CP3

Different Types of Parametrization for History-matching

One of the main goals of the reservoir characterization is toprovide geologically realistic reservoir property estimatesthat incorporate all relevant information. Preservation ofspatial structure is a crucial aspect of geologically realis-tic estimation. A key element in solving this issue is rep-resented by parameterization. Different types of param-eterizations are presented in combination with a historymatching algorithm

Remus G. HaneaTNO Built and Environment,remus.hanea@tno.nl

CP3

Sensitivity Analysis and Parameter Estimation inGroundwater Flows

In this work, we use Frechet derivatives of solutions ofgroundwater flow models with respect a hydraulic conduc-tivity parameter and demonstrate their applicability in es-timating this parameter from flow data; We will discuss thefact that the Frechet derivative operator is Hilbert-Schmidtand the implications for uncertainty quantification. Wewill use a power method and sensitivity equations to eval-uate the most significant directions and compute reducedrepresentations of the operator for efficient gradient calcu-lations.

Vitor Leite NunesInterdisciplinary Center for Applied MathematicsVirginia Polytechnic Institute and State Universityvitor@vt.edu

CP3

History Matching of Production and 4D SeismicData for a Realistic Sagd Case

We describe an assisted history matching method appliedto a realistic SAGD case. The objective is to constraina reservoir model with both production and P impedancevariations, derived from the stratigraphic inversion of a 4Dseismic dataset recorded over three years of production.We built a workflow with geological modeling, upscaling,flow simulation and petroelastic modeling to compute theproduction and seismic responses. Then, an optimizationprocess is run to minimize the data mismatch.

Elodie Tillier, Sebastien Da Veiga, Mickaele Le Ravalec,Axelle Baroni, Vincent Clochard, Karine Labat, OlivierLeratIFP Energies nouvellesElodie.Tillier@ifpenergiesnouvelles.fr,sebastien.da-veiga@ifpenergiesnouvelles.fr,mickaele.le-ravalec@ifpenergiesnouvelles.fr,axelle.baroni@ifpenergiesnouvelles.fr,

62 GS11 Abstracts

vincent.clochard@ifpenergiesnouvelles.fr,karine.labat@ifpenergiesnouvelles.fr,olivier.lerat@ifpenergiesnouvelles.fr

CP4

Near-Well Simulation in 3D Using Mpfa-Methods

Numerical simulation of fluid flow in a hydrocarbon reser-voir has to account for the presence of wells. We investigatenumerical schemes based on logarithmic grid refinementaround wells. In particular, multi-point-flux approxima-tion (MPFA) methods are investigated in three dimensions(3D) on different types of hybrid grids for the single phasepressure equation. The numerical experiments are used toprovide guidelines for selection of preferred grid and dis-cretization method for near-well simulation in 3D.

Haakon HaeglandCIPR, University of Bergen, Norwayhakon.hagland@uni.no

CP4

Sensitivity for Coupled Systems of Flow and Trans-port

We discuss several approaches to sensitivity analysis forcoupled systems modeling flow and transport in porous me-dia. The techniques include adjoint and global sensitivitymethods and the sensitivity equations. The applicationsinclude a transport model coupled to the flow with inertiaand a system of diffusion equations in heterogeneous mul-tiscale formations. Sensitivity analysis aids in the choiceof a reduced model which may decrease the computationalcomplexity.

Ken KennedyOregon State Universitykennedke@math.oregonstate.edu

Malgorzata PeszynskaDepartment of MathematicsOregon State Universitympesz@math.oregonstate.edu

CP4

Adaptive Mesh Refinement Algorithm for Simulat-ing Two-Phase Compressible Flow in Porous Media

We describe an adaptive mesh refinement (AMR) algo-rithm for simulating two-phase compressible flow in porousmedia under isothermal condition. The governing equa-tions are decomposed based on the total velocity split-ting approach to obtain a parabolic equation for the pres-sure and a set of hyperbolic equations for the componentdensities. This formulation forms the basis of a second-order sequential algorithm in which the pressure equa-tion is solved implicitly and the component conservationequations are solved explicitly. The algorithm is then im-plemented within a parallel block-structured AMR frame-work, enabling us to perform efficient large-scale simula-tions. To demonstrate features in the algorithm, we willexamine simulation results for an idealized model of a gasleaking from an underground LPG storage cavern.

George PauLBNLGPau@lbl.gov

John B. BellCCSELawrence Berkeley Laboratoryjbbell@lbl.gov

Ann S. AlmgrenLawrence Berkeley National LaboratoryASAlmgren@lbl.gov

Marc DayLBNLmsday@lbl.gov

Michael LijewskiLawrence Berkeley National Laboratorymjlijewski@lbl.gov

CP4

Mathematical and Numerical Study of a Two-Phase Two-Component Porous Media Model

We will present the mathematical existence of a degenerateparabolic system modeling two phase (liquid and gaz) twocomponent (water and hydrogen) flow in porous media inthe context of radioactive waste storage where the veloc-ity of the mass exchange between dissolved hydrogen andhydrogen in the gaz phase is supposed finite. We will alsopresent a numerical scheme to discretise this system andwe will present some properties for this numerical scheme.

Bilal SaadCEAbilal.saad@cea.fr

Mazen SaadEcole Centrale de Nantesmazen.saad@ec-nantes.fr

Florian CaroCEAflorian.caro@cea.fr

CP4

A Coupled Large-Scale Model for HydromechanicalSimulation of Co2 Geological Storage

A coupled hydro-mechanical modeling of CO2 injectioninto deep aquifers is proposed. Multiphase and multicom-ponent fluid flow is considered in interaction with the rockgeomechanical behaviour. The numerical methods used tolink a flow transport code and a mechanical code, in par-ticular fields transfer between non-coincident meshes andtime coupling algorithm, are then presented. Some resultsof large scale simulations especially some aspects of themechanical integrity of caprock are finally discussed.

Pierre SochalaBRGMp.sochala@brgm.fr

Vivien DesveauxUniversite de Nantes 2 rue de la Houssiniere44000 Nantesvivien.desveaux@univ-nantes.fr

Jeremy Rohmer, Darius SeyediBRGM 3 avenue claude guillemin

GS11 Abstracts 63

45000 Orleansj.rohmer@bgrm.fr, d.seyedi@brgm.fr

CP5

An Analytical Model for Transient Heat Flow inShallow Geothermal Systems

This contribution introduces a new analytical model ca-pable of simulating fully transient conductive-convectiveheat transfer processes in a shallow geothermal system con-sisting of a borehole heat exchanger embedded in a soilmass. The spectral analysis method is utilized. It calcu-lates the temperature distribution in all components usingthe discrete Fourier transform, for the time domain, andthe Fourier-Bessel series, for the spatial domain. Numeri-cal examples will be presented. See Al-Khoury, 2010, IJFF20, issue 7.

Rafid Al-KhouryCivil Engineering and GeosciencesDelft University of Technologyr.i.n.alkhoury@tudelft.nl

CP5

Elastic Response of Granular Soils with MultiscaleSubstructure

Effective medium theories for elastic and/or seismic re-sponse of granular soils have typically used theories such asHertz-Mindlin or Walton-type methods to determine over-all behavior. For environmental applications, it may alsobe necessary to consider smaller scale granularity due tobiomineralization. An important second scale of granu-larity arises when various forms of calcium carbonate areprecipitated on the soil grains, and near the regions of con-tact between soils grains. The strengthening effects can besignificant.

James G. BerrymanLawrence Berkeley National LabEarth Sciences DivisionJGBerryman@LBL.GOV

CP5

Characteristic Thermal Profiles in Open-LoopGeothermal Energy Harvesting

In exploring deep geothermal energy (> 2000 m), heatlosses in the boreholes can be significant and are depen-dent of the pumping rates, and sharp transitions in welldiameters and in geology. Temperature drops of 20-30 %between the top of the deep aquifer and ground surface arecommon. Quantifying these energy losses are fundamen-tal to determining the capabilities of the technology. Weformulate a mathematical model of the pipe-soil system inthe limit where axial convective transport within the pipebalances radial diffusion in the surrounding medium. Thisresults in a coupled system of boundary-value problems forsteady-state solutions, and the rates of thermal losses in theaxial direction are found as a function of the different piperadii and lengths, as well as the thermal properties of thesurrounding medium. Design choices for the pipe stagingare suggested based on the local geology of the site.

Burt S. Tilley, Miguel A. RascoMathematical Sciences DepartmentWorcester Polytechnic Institutetilley@wpi.edu, mrasco@wpi.edu

T BaumannInstitute of HydrologyTechnische Universitaet Muenchenthomas.baumann@ch.tum.de

CP5

How Phase Transition Is Affected by Chemical Po-tential and Relative Concentration

When we consider the phase transition of liquid to gaseouswater, relative humidity is considered the primary drivingforce. For adsorption/desorption, the relative concentra-tion of the species is considered the primary driving force.Theoretical considerations via Hybrid Mixture theory indi-cate that it is the difference between phase chemical poten-tials of the species which is the fundamental driving force.In this presenation we report preliminary theory on therelationship between chemical potential and the relativeconcentrations.

Eric R. Sullivan, Lynn Bennethum, Lincoln CollinsUniversity of Colorado Denvereric.sullivan@ucdenver.edu,lynn.bennethum@ucdenver.edu,lincoln.collins@email.ucdenver.edu

CP5

Numerical Solution to a Nonlinear TransportModel for Swelling Porous Materials

We demonstrate the results of a novel numerical schemeused to solve a coupled system of nonlinear transport mod-els consisting of a Volterra partial integrodifferential equa-tion of the second kind and a nonlinear diffusion equation.A model application is a drug delivery device consisting ofa drug interlaced within a polymer matrix. Results willbe shown for concentration profiles and moisture contentalong with an interpretation of viscoelastic effects presentin the model.

Keith WojciechowskiDepartment of Mathematical SciencesUniversity of Colorado DenverKeith.Wojciechowski@email.cudenver.edu

CP5

Numerical Method for Poroelasticity Based on aCoupling of Nonconforming and Mixed Finite Ele-ment Methods Using Rectangular Elements

In this talk, we present a finite element formulation to ap-proximate the coupled fluid and mechanics in deformableporous media. The method uses a nonconforming finiteelement for the displacement of the solid phase, and thelowest-order Raviart-Thomas mixed finite element for thepressure and the velocity of the fluid phase. To achievethe discrete Korn’s inequality, we add a penalty term tothe variational formulation. We provide a priori error es-timates.

Son-Young YiThe University of Texas at El Pasosyi@utep.edu

CP6

Existence of a Weak Solution for the Fully Coupled

64 GS11 Abstracts

Navier-Stokes/Darcy-Transport Problem

We study a surface/subsurface multiphysics problemarising from the problem of groundwater contamina-tion through rivers. Specifically, a convection-diffusiontype transport equation is coupled with the Navier-Stokes/Darcy flow via velocity field and concentration. Onthe interface, we accept balance of forces, continuity ofthe flux and the Beavers-Joseph-Saffman condition. Weanalyze this problem by proving the existence of a weaksolution by a method based on Galerkin approach in time.

Aycil CesmeliogluIMAaycil.cesmelioglu@ima.umn.edu

Beatrice RiviereRice UniversityHouston, Texas, USAriviere@caam.rice.edu

CP6

Permeability of Fluid Flow Through Cilia

This work concentrates on finding the permeability for vis-cous flow though a structure of periodic cylinders as a func-tion of cylinder density and cylinder angle. We use a fullthree-dimensional model of incompressible viscous fluid incombination with the Buckingham Pi Theorem to deter-mine the relationships. Numerical results are obtained us-ing Mixed Finite Element Method. The results are com-pared with Zick and Homsy (1982). Applications includemodeling the flow of mucus in lung tissue

Kannanut ChamsriUniversity of Colorado Denverwhychamsri@hotmail.com

CP6

Modelling of Tunnel Inflow with Complicated Dis-cretisation

We solve a 3D groundwater flow problem, predicting theinflow into a deep tunnel to fit the field measurement. Themain problem is a combination of a kilometer scale of thewhole model and a scale of the tunnel 3.6m diameter. Thisis done with sophisticated set mesh parameters, changingfrom 1m to 100m. We show comparisons with measureddata and also discuss possible solutions without explicitshape of the tunnel in the model geometry.

Milan Hokr, Ilona SkarydovaTechnical University of Liberec, FM NTImilan.hokr@tul.cz, ilona.skarydova@tul.cz

CP6

Smc Methods for the Calibration of StochasticRainfall-Runoff Models

The rainfall-runoff model considered in this talk is a con-ceptual stochastic model, formulated in contiuous-discretestate space form. We use a maximum likelihood approachbased on an EM algorithm. In this approach, the key ingre-dient is the computation of smoothed additive functionalsof hidden states (Olsson et al., 2008). Sequential MonteCarlo methods (SMC), also called particle methods, areused for smoothing in the state space model.

Franz Konecny

BOKU-University of Natural Resources and AppliedLife Sciences, Viennafranz.konecny@boku.ac.at

CP6

Solution of Time-DependentPde Through Component-Wise Approximation ofMatrix Functions

Krylov subspace spectral (KSS) methods have been demon-strated to be effective time-stepping methods for parabolicand hyperbolic variable-coefficient PDE. Their effective-ness stems from the use of different approximations for eachFourier component of the solution, based on techniquesfor approximating bilinear forms developed by Golub andMeurant. In this talk, it is shown how this essential in-gredient of KSS methods can be adapted to finite elementmethods that are applied to PDE that arise in reservoirsimulation.

James V. LambersUniversity of Southern MississippiDepartment of MathematicsJames.Lambers@usm.edu

CP6

Randomized Operator Fitting for Preconditioningthe Wave Equation Hessian

In this seminar, we consider the problem of approximatingthe inverse of the wave-equation Hessian, also called nor-mal operator, in seismic imaging. We develop an expan-sion scheme for the pseudodifferential symbol of the inverseHessian, and recover the coefficients via least-squares fit-ting from a certain number of applications of the normaloperator on adequate randomized trial functions. We showhow to construct these functions properly through analyt-ical considerations and the Curvelet transform. Once anapproximate inverse Hessian is available, application to animage of the model can be done in very low complexity.We also present numerical experiments demonstrating theperformance of the method.

Pierre-David LetourneauStanford Universitypletou1@stanford.edu

Laurent DemanetMathematics, MITdemanet@gmail.com

CP6

An Adaptive Approach for Simulation of Flow Ac-cumulation; a Mathematical Modification of RmmfModel

Simulation of flow accumulation with available GIS soft-ware to use in the Revised-Morgan Morgan-Finny modelcauses high overestimation of erosion at large scales (catch-ment or regional). The provided remedy was implementingharmonic and P-series in calculation of distributed runofffor simulating flow accumulation. Results showed thaterror in Harmonic-series approach was considerably de-pendent on slope length, whereas in P-series formulationremained less than 10% for various slope lengths. Theaccumulation of runoff along the slope was validated bymeasured discharge within Namchun watershed, Thailand,which was acceptable according to Morgan 2005. The

GS11 Abstracts 65

study revealed that through the new modification, theRMMF model can be a useful empirical-physically-basedmodel in erosion assessment at large scale.

Khatereh PolousITC Institute, Twente University, The Netherlandspolous21294@itc.nl

Amir HooshmandInstitute for Advanced StudyTechnical University of Munich, Germanyamir.hooshmand@pe.mw.tum.de

Yousef HooshmandInstitute for Product EngineeringUniversity of Duisburg-Essen, Germanyyousef.hooshmand@uni-due.de

CP7

Short Wave Instabilities in Free Surface ShearFlows

In this study, We investigate the linear stability of inviscidplane Poiseuille flow between two parallel free surfaces. Weshow that there are short wave instabilities with eigenfunc-tions localized near the free surface and derive the asymp-totics of these modes. The stability of wall bounded in-viscid shear flows has been studied for more than a cen-tury. However, shear flows bounded by free surfaces arealso a solution of the Euler equations. Although there areentire books on stability of films and jets, these studieshave focussed on instabilities due to surface effects, suchas surface tension and air drag, and they usually assume auniform velocity within the jet or film. They consider anaxisymmetric jet bounded by a free surface with a Hagen-Poiseuille profile of the velocity. They conclude that thenonuniform velocity in the jet has a stabilizing effect. Thisconclusion, however, is due to their failure to consider non-axisymmetric modes. In recent work by M. Renardy, it wasshown that plane parallel shear flows bounded by two freesurfaces have long wave instabilities for all velocity profilesthat are not uniform. This is in marked contrast to the wallbounded case, where criteria such as those of Rayleigh andFjortoft guarantee stability of a broad class of flows. Inthis work, we shall show that some flows, such as planePoiseuille flow, also have short wave instabilities. Again,this is in marked contrast to the wall bounded case. In thiscase, no smooth velocity profiles unstable to short wavesare known, and for certain classes of flows there are evenresults ruling out short wave instability.

Ahmed Kaffelvirginia techkaffel07@gmail.com

CP7

Analysis and Numerics of the Magnetohydrody-namic Equations for Real Gases

We present an analytical study of the wave structure of theMHD equations for real gases based on the local decompo-sition in characteristic wavefields. We propose a completesystem of eigenvectors that guarantees continuity with re-spect to the conserved variables in the neighborhood ofsingular points. We formulate a high order characteristic-based entropy-fix upwind numerical scheme based on theanalytical study. Numerical examples show good accuracy

and stability under high CFL numbers.

Susana SernaDepartment of MathematicsUniversitat Autonoma de Barcelonaserna@mat.uab.es

CP7

Constrained Optimization Schemes for 1D InverseWave Propagation Problems

We compare three constrained optimization schemes forsolving 1D inverse wave propagation problems posed asPDE-constrained optimization programs. Our goal is toidentify the best scheme that incorporates inequality con-straints over the model parameter, i.e. shear modulus, tobe used in conjunction with a robust algorithm that solvesthe inverse problem. We conduct a numerical experimen-tation for each method with synthetic problems, createdbased on velocity models derived from seismic measure-ments, and report their performance.

Anibal SosaThe University of Texas at El PasoComputational Science Programusosaaguirre@miners.utep.edu

Leticia VelazquezThe University of Texas at El PasoDepartment of Mathematical Sciencesletivela@gmail.com

Carsten BursteddeThe University of Texas at Austincarsten@ices.utexas.edu

Miguel ArgaezUniversity of Texas at El pasomargaez@utep.edu

Omar GhattasUniversity of Texas at Austinomar@ices.utexas.edu

CP8

A Sigma-Coordinate, Discontinuous GalerkinMethod for the Three-Dimensional Shallow WaterEquations

In this presentation, we describe the development, imple-mentation, and application of a novel sigma–coordinatediscontinuous Galerkin (DG) method for the three–dimensional shallow water equations. The h (mesh) and p(polynomial order) convergence properties of the methodare demonstrated on a set of analytic test cases. The devel-opment of new efficient (in some cases optimal) cubaturerules for integration over triangular prism elements is alsodiscussed.

Ethan KubatkoDepartment of Civil and Environmental EngineeringThe Ohio State Universitykubatko.3@osu.edu

Clint DawsonInstitute for Computational Engineering and SciencesUniversity of Texas at Austinclint@ices.utexas.edu

66 GS11 Abstracts

Ashley Maggi, Colton ConroyThe Ohio State Universitymaggi.1@osu.edu, conroy.51@osu.edu

CP8

Large Time Step Finite Volume Evolution GalerkinSchemes for Shallow Water Flows

We present two new large time step methods within theframework of the well-balanced finite volume evolutionGalerkin (FVEG) schemes. The methodology will be il-lustrated for low Froude number shallow water flows withsource terms modeling the bottom topography and Coriolisforces, but results can be generalized to more complex sys-tems of balance laws. The FVEG methods couple a finitevolume formulation with approximate evolution operators.The latter are constructed using the bicharacteristics ofmultidimensional hyperbolic systems, such that all of theinfinitely many directions of wave propagation are takeninto account explicitly. This is a novel feature of our FVmethod. As a result the FVEG schemes are typically 10times more accurate than standard FV schemes. In orderto approximate multiscale phenomena we have developedtwo variants of large time step FVEG method: a semi-implicit time approximation and an explicit time approxi-mation using several evolution steps along bicharacteristiccones. Behaviour of new FVEG schemes will be illustratedon a set of numerical experiments.

Maria LukacovaUniversity of MainzInstitute of Mathematicslukacova@mathematik.uni-mainz.de

Anna Hundertmark, Florian PrillInstitute of Mathematics, University of Mainzhundertm@uni-mainz.de, prill@uni-mainz.de

CP8

Numerical Modeling of Surface Flows Based onMulti-Dimensional Models and Variational DataAssimilation. Application to Flood Plain Flows

In geophysical flows such as surface water flows, multi-scales features and uncertainties of input parameters (egtopography, parametrization of empirical laws) invite toderive multi-dimensional models (or multi-scale models likeshallow-water / ALE free surface) while comparing the nu-merical results to observations. We present a global al-gorithm based on optimal control and adjoint equationswhich makes fit the coupled multi-dimensional (or multi-scales) models with heterogeneous data (in-situ, remote-sensed).

Jerome MonnierMathematics Institute of Toulousejerome.monnier@insa-toulouse.fr

CP8

Study of Overland Flow with Uncertain InfiltrationUsing Stochastic Tools.

Saturated hydraulic conductivity is a key parameter inoverland flow models with infiltration, but several studieshave shown the difficulty to correctly measure or estimatethis parameter. We therefore propose to consider this pa-rameter as a stochastic input parameter. We use a MonteCarlo method to quantify uncertainty propagation and to

study using Sobol indices the sensitivity of model resultsto the value and the spatial distribution of saturated hy-draulic conductivity along a slope.

Marie RousseauUniversite Paris-Est, CERMICS - ENPCBRGMma.rousseau@brgm.fr

Olivier CerdanBRGMo.cerdan@brgm.fr

Alexandre ErnUniversite Paris-EstCERMICS, Ecole des Pontsern@cermics.enpc.fr

Olivier Le MatreLaboratoire d’Informatique pour la Mecanique et lesSciencesLIMSI-CNRSolm@limsi.fr

Pierre SochalaBRGMp.sochala@brgm.fr

CP8

Effects of Shear Flow on KdV Balance, with Ap-plications to Tsunami

Building upon recent work on the applicability of KdV totsunami propagation, we discuss the effects of shear flow onthe KdV balance. This leads in the shallow-water limit tothe Burns condition which determines propagation speedsthat arise in the KdV balance. For waves propagatingcounter to the shear, KdV dynamics arise earlier, whilethey arise later for waves propagating with the shear, themagnitude of this effect depending on surface shear veloc-ity.

Raphael StuhlmeierFaculty of Mathematics, University of Viennaraphael.stuhlmeier@univie.ac.at

CP8

Semi-Implicit Finite Volume Schemes for ShallowFree Surface Flows

We address the derivation of FV schemes for thin film flowswith low Froude number (eg surface water flows), and withpotential wet-dry front. We present and analyze a newsemi-implicit scheme, unconditionaly stable and robust, forunviscid shallow-water models. Numerical examples arepresented in a river hydraulics context, w/wo over-flowing(flood plain).

Jean-Paul VilaMathematics Institute of Toulousevila@insa-toulouse.fr

CP9

Stable Algorithms for a Two Domain Natural Con-vection Problem and Observed Model Uncertainty

Numerical algorithms are studied for a Boussinesq model ofnatural heat convection in two domains, motivated by the

GS11 Abstracts 67

dynamic core of climate models. One algorithm is coupledacross the ?uid-?uid interface. Another is decoupled usinga partitioned time stepping approach that retains uncon-ditional stability. An empirical study of model uncertaintyis presented where stochastic noise is introduced into twononlinear coupling terms that play an important role instability.

Jeffrey M. ConnorsLawrence Livermore National LaboratoryCenter for Applied Scientific Computingconnors4@llnl.gov

Benjamin GanisUniversity of Texas at AustinCenter for Subsurface Modelingbganis@ices.utexas.edu

CP9

Time-dependent Wellbore Index Pressure Calcula-tions

We discuss a new post-processing technique for stan-dard reservoir simulators to determine detailed informationabout the time-dependent pressure at a wellbore. This in-formation is used in well test analysis. Standard simulatorsuse point or line source well models and do not resolve downto the tiny scale of the well radius. Our method involvesjust a local solve of the time dependent pressure equationin the vicinity of the wellbore, using as boundary data in-formation from the main reservoir simulation. We describethe connection with the Peacemann wellbore index, discussthe accuracy and show results from a number of test cases.

Dugald Duncan, Nneoma OgbonnaHeriot-Watt Universityd.b.duncan@ma.hw.ac.uk, nneoma08@hotmail.com

CP9

On a Distribution of the Enkf Sampling Error

Ensemble Kalman filter is a state space ensemble-based for-mulation of the Kalman filter. It is based on a low-rank co-variance approximation from a moderately sized ensemble.Sampling errors lead to artificial effects, such as spuriouscorrelations, deteriorating the estimates and the forecastsof the system states. We derive the distribution of the sam-pling error for the EnKF after a single analysis step. Thedistribution depends on ensemble size, model dimensionand observation locations.

Andrey KovalenkoCenter for Integrated Petroleum ResearchUniversity of Bergenandrey.kovalenko@uni.no

Trond MannsethCenter for Intergrated Petrleum ResearchUniversity of Bergentrond.mannseth@uni.no

Geir NvdalInternational Research Institute of Stavanger& Centre of Integrated Petroleum Research, UoBgeir.naevdal@iris.no

CP9

Modeling of Uncertainty for a Spatial SimulatorResponse

Complex numerical models such as oil reservoir simula-tor involves lots of uncertain input parameters (geological,fluid flow parameters...) and can yield spatial outputs likeoil saturation maps. To compute sensitivity analysis anduncertainties studies, experimental design and metamodelsare used. We propose an innovative strategy based uponthe wavelet decomposition of the output, the optimal se-lection of wavelet coefficients and their metamodeling bythe Gaussian processes. An application on an oil reservoirillustrates the methodology.

Amandine Marrel, Mathieu FerailleIFP Energies nouvellesamandine.marrel@ifpenergiesnouvelles.fr,mathieu.feraille@ifpenergiesnouvelles.fr

CP9

Multiscale Wavelet-Analysis-Based Localization ofCovariance Estimates in the Ensemble Kalman Fil-ter

In the ensemble Kalman filter, a sequential Monte Carlomethod for Bayesian inversion, covariances are estimatedfrom a small ensemble. There, sampling errors manifestin spurious, long-range correlations. In this work we dis-cuss a new method to reduce the negative impact of suchcorrelations. It is designed for inversion problems wherethe forward model contains significant features on multi-ple scales, e.g. history matching of hydrocarbon reservoirs.Different scales are resolved by a multi-scale wavelet trans-form.

Oliver PajonkInstitute of Scientific ComputingTechnische Universitat Braunschweigo.pajonk@tu-bs.de

Ralf Schulze-RiegertSPT Group GmbHralf.schulze-riegert@sptgroup.com

Hermann G. MatthiesInstitute of Scientific ComputingTechnische Universitat Braunschweigwire@tu-bs.de

CP9

Stochastic Parameterizations of Highly Heteroge-neous Media

We discuss new approaches to stochastic parameterizationsof flow in porous media based on Karhunen-Loeve, Haar,and other series expansions appropriate for highly hetero-geneous media. Of particular interest are parameteriza-tions for discontinuous and multiscale porous media as wellas interpretations of data simulated with geostatistics pack-ages such as GSLIB. We use these parameterizations in fi-nite element algorithms to compute moments of variablesof interest such as pressures and fluxes.

Veronika S. Vasylkivska, Malgorzata Peszynska, MinaOssianderDepartment of MathematicsOregon State Universityvasylkiv@math.oregonstate.edu,

68 GS11 Abstracts

mpesz@math.oregonstate.edu,ossiand@math.oregonstate.edu

CP10

Operator Splitting For Advection Diffusion Equa-tions with Discontinuous Coefficients

We consider time dependent advection diffusion equationswith discontinuous diffusion coefficient. Using an opera-tor splitting methodology we develop a fictitious domainmethod to numerically solve the time dependent diffusionequation. For the advection part we use a dispersion op-timized nonstandard finite difference method that enablesfollowing the transport and tracking sharp fronts more ac-curately. The problems addressed here are motivated byapplications combining the transport, growth and decay ofbiological/chemical species in heterogeneous landscapes.

Vrushali A. BokilOregon State Universitybokilv@math.oregonstate.edu

CP10

Direct Numerical Simulation of Inertial in PourousMedia

At modest flow rates (Re > 100) through porous me-dia and packed beds, fluid inertia can result in complexsteady and unsteady recirculation regions, dependent onthe local pore geometry. As a result of fluid intertia, flowthrough porous media and packed beds can develop com-plex steady and unsteady recirculation regions at modestflow rates (Re > 100). We investigate these inertial flowregimes using (i) a body-fitted unstructured grid Navier-Stokes solver [Moin and Apte, AIAA J. 2006], and (ii) afictitious domain based finite-volume approach [Apte et al.JCP 2009], wherein non-body conforming Cartesian gridsare used and the no-slip boundary conditions on the poreboundaries are enforced implicitly through a rigidity con-straint force. For the body-fitted unstructured grid ap-proach, we present methods to parameterize and simplifymesh generation for packed beds, with an eye toward ob-taining efficient mesh independence for Reynolds numbersin the inertial and unsteady regimes. To handle the ge-ometric singularity at the sphere-sphere and sphere-wallcontact points, we use a fillet bridge model, in which everypair of contacting entities are bridged by a fillet, eliminat-ing a small fluid region near the contact point. A secondorder accurate, parallel, incompressible flow solver is usedto simulate flow through three different sphere packings:a periodic simple cubic packing, a wall bounded hexag-onal close packing, and a randomly packed tube. Meshindependence is assessed using several measures includingErgun pressure drop coefficients, viscous and pressure com-ponents of drag force, kinetic energy, kinetic energy dissi-pation and interstitial velocity profiles. Direct comparisonsof the body-fitted and the fictitious domain approaches aremade to evaluate the accuracy of the latter approach forsimulation of flow through complex configurations observedin randomly packed beds.

Sourabh V. Apte, Justin FinnOregon State Universitysva@engr.orst.edu, finnj@engr.orst.edu

CP10

Direct Numerical Simulations of Solid-Fluid Cou-

pling in Geophysical Systems

Numerous problems in the Earth sciences involve the dy-namic interaction between solid bodies and viscous flow.While modelers are well equipped to deal with the end-member cases of predominantly liquid or solid systems, theintermediary regime remains challenging. We develop anew computational methodology for simulating solid-fluidinteractions based on distributed Lagrange multipliers andapply our approach to investigate the competing effects ofentrainment and sedimentation of crystals during magmacooling.

Jenny SuckaleMassachusetts Institute of Technologysuckale@mit.edu

James SethianUniversity of California, BerkeleyDepartment of Mathematicssethian@math.berkeley.edu

Jiun-Der YuEpson Research&Development Inc.jdyu@erd.epson.com

Linda Elkins-TantonMITltelkins@mit.edu

CP10

Simulation of Pore Scale Precipitation and Disso-lution Using Adaptive, Finite Volume Methods

Precipitation (or dissolution) of mineral grains modifiesthe geometry of the pore space in subsurface sedimentwith continuously evolving solid-liquid boundaries. Inturn, changes in the pore space alter the groundwater flowthrough the sediment, which ultimately affects the contin-uum scale reaction rates that are relevant for field appli-cations such as carbon sequestration. Modeling provides aunique tool to understand and quantify the feedback pro-cesses between mineral precipitation (or dissolution) andflow at the pore scale. Higher-order algorithms based onadaptive mesh refinement and finite volume methods havebeen successfully applied to flow and reactive transport incomplex microscale geometries such as microarray chan-nels. Here, we couple a geochemical module that includesaqueous complexation and mineral reactions to a new flowand transport simulation capability based on adaptive, fi-nite volume methods. We have also extended this frame-work to track moving solid-fluid interfaces as a result ofmineral reactions. This approach is consistent with thoseused for moving fluid-fluid interfaces, providing a robustand algorithmically consistent methodology for multiphaseflow. We show that these advanced methods offer a promis-ing alternative for reactive pore scale modeling throughsimulations of single pore throats as well as packed beds.

David Trebotich, Sergi Molins, Carl SteefelLawrence Berkeley National Laboratorytreb@hpcrd.lbl.gov, smolins@lbl.gov, cisteefel@lbl.gov

CP10

Title Not Available at Time of Publication

Multiscale methods have received significant attention inrecent years. Multiscale formulations, however, have notyet reached the robustness and applicability range nec-

GS11 Abstracts 69

essary for general-purpose reservoir simulation practice.Here, we address two aspects associated with highly het-erogeneous models that pose a serious challenge to existingmultiscale finite-volume formulations, namely, channel-likefeatures and strongly anisotropic transmissibility (tensorpermeability, high aspect ratio). We describe a Two-stageAlgebraic Multiscale Solver (TAMS) for the pressure linearsystem. One stage deals with a global coarse-grid prob-lem, which is constructed using prolongation and restric-tion operators. The prolongation operator is assembledfrom the multiscale basis functions. The restriction oper-ator is either the transpose (i.e., Galerkin coarsening), ora conservative scheme. The second stage uses a local pre-conditioner (e.g., Block Incomplete LU) on the fine-grid.TAMS is guaranteed to converge to the fine-grid solutionwith a computational cost superior to existing state-of-the-art approaches, such as Algebraic MultiGrid (AMG). Thus,TAMS can be used as linear-solver for the pressure equa-tion. TAMS also guarantees conservation after every it-eration; so, TAMS can serve as an approximate pressuresolver in a conventional simulator, where the results areused to perform transport computations.

Hui ZhouStanford Univ.huizhou@stanford.edu

CP11

Multilevel Simulation and a-Posteriori Estimatorsfor Double-Porosity Models

Double porosity models are useful for modeling flow anddiffusion in highly heterogeneous media of binary charac-ter. The well-known Barenblatt and Warren-Root modelsare actually asymptotic limits of models of tertiary struc-ture, and the latter can be seen as a special case of the for-mer. We present numerical solutions on multilevel meshesfor these models and propose an appropriate a-posteriorierror estimator which is robust in the parameters and al-lows to compare the models.

Viviane KleinOregon State Universitykleinv@math.oregonstate.edu

Malgorzata PeszynskaDepartment of MathematicsOregon State Universitympesz@math.oregonstate.edu

CP11

Special Functions to Capture Spatial Heterogeneityfor Diffusion Equation with Decay

In this talk we discuss on developing special shape func-tions for diffusion with decay that capture underlying het-erogeneity of the medium. We show that generating shapefunctions using homogeneous differential equation (whichis the standard way of generating special functions un-der the Multiscale Finite Element Method) will not sat-isfy the partition of unity property for the chosen equa-tion. Herein, we consider an alternate (non-homogeneous)boundary value problem for generating shape functionsthat ensures Kronecker-delta and partition of unity prop-erties. In addition, if the medium is homogeneous, we re-cover the standard shape functions for that particular fi-nite element under the proposed method. Another novelfeature of the proposed methodology is that the resultingsolution satisfies maximum principles and the non-negative

constraint on general computational grids with low-orderfinite elements. This is achieved by augmenting the un-derlying variational principle with appropriate constraints(which will be in the form of inequalities). The resultingproblem belongs to convex quadratic programming, whichis solved using active-set strategy. Representative numeri-cal examples are presented to show the overall performanceof these special shape functions, and their ability to re-solve the heterogeneity of the medium using coarse com-putational grids. We also present numerical convergencestudies of the proposed methodology with respect to re-finement of both coarse- and fine-scale meshes. This workis in collaboration with Professor Albert Valocchi (UIUC)and M. K. Mudunuru (Texas A&M University).

Kalyana NakshatralaTexas A&M Universityknakshatrala@tamu.edu

CP11

Reactive Transport Simulation with EmbeddedDiscontinuity in Fractured Porous Media

Material discontinuities in fractured porous media stronglyinfluence single/multiphase fluid flow. When continuummethods are used to model transport across material in-terfaces, they smear out jump discontinuities of concentra-tion or saturation. To overcome this problem, we split thefinite-element models with complementary node-centredfinite-volumes along the material interfaces, developing atransport scheme that represents the dependent variablediscontinuities arising at these interfaces. We have foundthat using the discontinuous scheme is crucial to capturethe emerging patterns due to the interaction of heterogene-ity, and reactive transport.

Hamid M. NickDepartment of Earth Sciences - GeochemistryUtrecht Universitynick@geo.uu.nl

Pierre RegnierBiogeochemical Modeling of the Earth SystemUniversite Libre de Bruxellesp.regnier@geo.uu.nl

Martin ThullnerDepartment of Earth Sciences - GeochemistryUtrecht Universitymartin.thullner@ufz.de

Stephan K. MatthaiMontan University of LeobenLeoben, Austriastephan.matthai@gmail.com

Florian CentlerDepartment of Environmental MicrobiologyHelmholtz Centre for Environmental Research - UFZflorian.centler@ufz.de

CP11

Mixed Multiscale Basis Functions for Iterative Do-main Decomposition Procedures

We discuss the development of a multiscale method forthe solution of the heterogeneous Poisson’s equation thatcan take advantage of state-of-the-art CPU-GPU proces-

70 GS11 Abstracts

sors. We consider non-overlapping and overlapping do-main decomposition procedures for mixed finite elementdiscretizations of the elliptic equation with discontinuouscoefficients. Mixed multiscale basis functions with Robin-type boundary conditions are proposed. Computationalefficiency is achieved through a careful selection of sub-spaces of the space spanned by these basis functions forapproximating local problems.

Alexandre FranciscoUniversidade Federal Fluminenseafrancisco@metal.eeimvr.uff.br

Victor E. GintingDepartment of MathematicsUniversity of Wyomingvginting@uwyo.edu

Felipe PereiraCenter for Fundamentals of Subsurface FlowUniversity of Wyominglpereira@uwyo.edu

Joyce RigeloUniversity of Wyomingjrigelo@uwyo.edu

CP11

Effective Behavior of Flow and Transport Parame-ters at Different Scales in Spatially HeterogeneousPorous Media Without Scale Separation

We investigate the effective behavior of hydraulic con-ductivities and mixing coefficients in heterogeneous mediawithout scale separation. The covariance function of thelog hydraulic conductivity can be modeled by an algebraicfunction. The exponent of this power law is chosen that nofinite integral length exists. Such functions can be writtenas a superposition of Gaussian covariance functions withfinite correlation lengths. We give explicit expressions andcoarse graining results for flow and transport parameters.

Katharina RossInstitute of GeosciencesUniversity of Jenakatharina.ross@uni-jena.de

Sabine AttingerInstitute of Computational ComputationalEnvironmentaScienceUFZ Leipzigsabine.attinger@ufz.de

CP11

On Flows Through Deformable Laminates

Fluid flows through anisotropic media are found in awide variety of geophysical and biological systems. Themacroscale behavior of these systems depend on the un-known microstructure, which depend on the local physicalprocesses. As a first model, we consider the flow of anincompressible fluid that saturates an array of deformablelaminates with gravity acting in the spanwise direction.The aspect ratio of the characteristic spacing between thelaminates is much smaller than the characteristic scale ofthe laminate length, and we use this aspect ratio to findeffective equations for the components of the stress tensorof the effective material. Compatibility conditions at lead-

ing order result in a coupled set of elliptic equations forthe unknown laminate spacing and the local pore pressure.Effective stress-strain relations are derived based on the lo-cal geometry and material properties of the laminates andfluid.

Burt S. Tilley, B VernescuMathematical Sciences DepartmentWorcester Polytechnic Institutetilley@wpi.edu, vernescu@wpi.edu

J. PlummerCivil and Environmental Eng. Dept.Worcester Polytechnic Institutejplummer@wpi.edu

CP12

Leveraging the General-Purpose Computation onGraphics Processing Units (gpgpu) Architecturefor Lidar Data Processing

Processing datasets associated with LiDAR mappings isprohibitive due to the large datasets and computationalnature of the processing. This is particularly problematicwhen working to achieve interactive or real-time data ma-nipulation. By leveraging GPGPUs and reevaluation of thecomputational algorithms used in the processing of largeLiDAR datasets we are able to accelerate the dataminingprocess. Our results reflect aspects of GPGPU environ-ments that achieve significant speedups (and slowdowns)when ported to the GPGPU environment.

Paul GrayUniversity of Northern IowaComputer Sciencegray@cs.uni.edu

Dossay Oryspayev, Ramanathan SugumaranUniversity of Northern Iowado515256@uni.edu, sugu@uni.edu

CP12

A Comparison of Parallel Preconditioners for theMixed Finite Element Solution of Darcy’s Equation

Darcy flow in a heterogeneous medium can be accuratelycomputed with mixed finite elements. Hybridization leadsto a positive definite system, solved by an iterative method.The LifeV finite element library,developped by EPFL,MOX and INRIA, relies on Trilinos for solving the lin-ear system. Trilinos includes parallel iterative solvers, andpreconditioners based on one level Schwarz (IFPACK) andparallel multi-level methods (ML). We compare the effi-ciency and parallel scalability of these preconditioners forsolving Darcy flow.

Michel KernINRIAmichel.kern@inria.fr

Alessio FumagalliMOX, Politecnico di MilanoItalyalessio.fumagalli@polimi.it

CP12

Numerical Modeling of Flow Through Porous

GS11 Abstracts 71

Structures and Vegetated Regions

Due to computational constraints, when modeling incom-pressible flow over and around porous structures or throughheavily vegetated regions one must often use upscalingtechniques to find parameterizations for resistance due toform drag. We analyze and perform theoretical and compu-tational upscaling techniques for flows ranging from thosewith very small Reynolds numbers to those that are tur-bulent through a variety of 2D and 3D domains.

Steven A. MattisThe Institute for Computational Engineering and SciencesUniversity of Texas at Austinsteven@ices.utexas.edu

Clint DawsonInstitute for Computational Engineering and SciencesUniversity of Texas at Austinclint@ices.utexas.edu

Chris KeesU.S. Army Engineer Research and Development CenterCoastal and Hydraulics Laboratorychristopher.e.kees@usace.army.mil

Matthew FarthingUS Army Engineer Research and Development Centerqmatthew.w.farthing@usace.army.mil

CP12

From a Coarse-Scale Flow Model to Fine-Scale Per-meability Identification

We apply an inverse modeling approach to determine fine-scale permeabilities based on heads - flow rates pairs com-puted on the level of a coarse-scale model. This fits intoa downscaling framework if we assume that coarse scalepermeabilities are actually determined within an upscal-ing scheme. In our approach a double constraint methodis used, based on finite element discrete approximations.The results obtained apply to models with anisotropy ef-fects.

Anna TrykozkoUniversity of Warsawaniat@icm.edu.pl

MS1

On a LES-deconvolution Model for the Ocean witha Fixed Wind

Kolmogorov’s theory predicts that simulating turbulentflows by using the Navier-Stokes Equations requires R9/4

degrees of freedom, where R is the Reynolds number.Thisnumber is too large to perform a Direct Numerical Simu-lation. This is why one aims at computing mean values ofthe flows field. The case that we study is an oceanic basinwith a fixed wind. We consider means obtained by convo-lutions like in usual Large Eddy Simulation models. Weintroduce the concept of deconvolution model that aimsat reconstructing the true flow field by regenerating highfrequency wave numbers when the numerical mesh has afixed size. We summerize some mathematical results andfinally show numerical simulations in an oceanic basin witha given fixed wind, using the deconvolution concept.

Roger LewandowskiIRMAR, UMR 6625

Universite Rennes 1Roger.Lewandowski@univ-rennes1.fr

MS1

Large Eddy Simulation of Mixing in StratifiedFlows

Mixing is a challenging quantity to get right accurately, yetit is important for many oceanic processes and the generalcirculation. Performance of various eddy-viscosity and ap-proximate deconvolution type subgrid-scale models (SGS)in LES is evaluated in the lock-exchange problem, whichcontains shear-driven mixing, internal waves, interactionswith boundaries and convective motions, while having asimple domain, initial and boundary conditions, and forc-ing. The measure of the comparison taken as the back-ground potential energy and DNS results at 103 ≤ Re ≤104 are used as benchmarks. By relying on the best-performing SGS models, estimates of mixing at higher Reare provided.

Tamay Ozgokmen

University of Miami/RSMAStozgokmen@rsmas.miami.edu

Traian IliescuInterdisciplinary Center for Applied Mathematicsiliescu@vt.edu

Paul F. FischerUniversity of California, Irvine andWeizmann Institute of Science, Israelfischer@mcs.anl.gov

MS1

A New Projection Method for Separating Surfaceand Interior Modes in Oceanic Data

A number of recent studies have demonstrated that al-timetric observations of the ocean’s mesoscale eddy fieldreflect the combined influence of both surface buoyancyanomalies and interior potential vorticity anomalies. Theformer are associated with surface-trapped modes, withan exponentially-decaying vertical structure, and the lat-ter with the standard baroclinic modes, the oscillatingeigenfunctions of the quasigeostrophic potential vortic-ity stretching operator. In order to assess the relativeimportance of the two contributions to the signal, onewould like to project the observed field onto a set ofcomplete modes that separates the influence of each as-pect of the dynamics in a natural way. However, becausethe surface-trapped solutions are dependent on horizon-tal wavenumber, they are not, in general, orthogonal tothe (wavenumber-independent) interior baroclinic modes,thus any combined projection will contain energetic over-laps. Here we propose a generalization of potential vor-ticity that includes surface buoyancy anomalies (akin toBretherton’s generalized form, but without the use of nu-merically ill-defined delta-functions), and compute its ver-tical eigenfunctions for each horizontal wavenumber. Theseeigenfunctions provide a set of mutually-orthogonal modesthat reflect surface and interior components naturally. Wecompute these modes for a given stratification, and demon-strate their use by projecting out the energy of a set ofhigh-resolution, eddying simulations.

Shafer SmithCenter for Atmosphere Ocean ScienceCourant Institute

72 GS11 Abstracts

shafer@cims.nyu.edu

Jacques VannesteSchool of MathematicsUniversity of EdinburghJ.Vanneste@ed.ac.uk

MS1

Suitable Boundary Conditions for the Shallow Wa-ter Equations in a Limited Domain.

In this lecture we will discuss two issues of general interestin scientific computing, namely: - Numerical simulationsin a limited domain when the boundary conditions are notwell defined at the boundary, and, - The use of multilevelmethods for solving partial differential equations. Bothproblems will be discussed in the context of the inviscidshallow water equations.

Roger M. TemamInst. f. Scientific Comput. and Appl. Math.Indiana Universitytemam@indiana.edu

Arthur Bousquet, Ming-Cheng ShiueIndiana Universityarthbous@indiana.edu, mshiue@indiana.edu

MS2

An Asymptotic Description of the Interactionfo Waves on the ITCZ with Midlatitude Quasi-geostrophic Dynamics

In a ground breaking paper, Majda & Klein introducedtwo new dynamical regimes describing the tropical tropo-sphere. The first regime, IPESD provides a framework forthe recent multiscale models of the Madden-Julian oscil-lation. The second regime, the mesoscale equatorial weaktemperature gradient (MEWTG), describes a circulationforced by latent heating due to moist convection. Theweak temperature gradient feature of this regime impliesthat diabatic heating balances vertical velocity on equa-torial mesoscales, O(500km), and within timescales of lessthan one day. Majda recognized that this new multiscaleMEWTG is a closed model by going to higher order inthe asymptotics. The resulting model contains the origi-nal MEWTG equations modulated by a large scale, zon-ally propagating gravity wave. The temperature and windproperties of the large scale wave are independent of boththe zonal and meridional mesoscales and are, thereby, con-sistent with the weak temperature gradient nature of thetropics. The mean zonal winds described by the multiscaleMEWTG equations become unbounded at large latitudesaway from the equatorial belt. Unless specific restrictionsare made on the mean of the diabatic heating, the the-ory also yields solutions with non-zero meridional velocitiesfar from the equatorial belt; i.e. an open Hadley circula-tion. Furthermore, meridional geostrophic balance is notdescribed by this theory, yet this is known to be the mainbalance for subtropical and midlatitude winds. We derivematching condition to the subtropics which closes the mul-tiscale MEWTG theory and connects the equatorial flowswith midlatitude dynamics.

Joseph A. BielloUniversity of California, DavisDepartment of Mathematicsbiello@math.ucdavis.edu

Andrew MajdaCourant Institute NYUjonjon@cims.nyu.edu

MS2

Stochastic Models for Tropical Convection: FromIdealized Conceptual Models to GCM Simulations

Large scale models that are used for longterm weatherforecast and climate prediction are based on a coarse dis-cretization of the governing equations with a grid spacingvarying from 50 km to 200 km. For a such complex sys-tem –the Earth-ocean-atmosphere system, many importantprocesses such clouds, radiation, air sea interaction, vege-tation, and boundary layer turbulence, remain unresolved;they are represented by various recipes known as param-terizations. However, most of these parametrizations suchas those pertaining to clouds and atmospheric convectionare based on equilibrium closures that are hardly testedand in most cases underestimate the dynamics due to veryintermittent local interactions at small scales. In this talkwe will discuss a hierarchy of stochastic models that rep-resent various unresolved physical processes, and their ef-fect on the large-scale resolved variables, ranging from con-vective inhibition, using an Ising-type spin flip model, tomulti-state Markov chains for organized tropical convec-tion consisting of three cloud types, congestus, deep, andstratiform. The models are first test on simple toy mod-els where their intrinsic features are explored and their pa-rameters calibrated then more recently implemented in thecontext of more comprehensive atmospheric general cir-culation models that are used for operational long termweather and climate predictions.

Boualem KhouiderUniversity of VictoriaDepartment of Mathematicskhouider@math.uvic.ca

MS2

A Potential Vorticity Dynamics for Rotating Shal-low Water on the Sphere

The evolution of weather systems in the midlatitude at-mosphere is well-explained by the theory of quasigeostro-phy (QG), in which slow, synoptic-scale airflows are de-scribed through the advection of potential vorticity (PV).The mathematics of QG is often justified by a limit of smallRossby number. However, this assumed limit is made in-valid across the equator by the vanishing of the Corioliseffects. A globally-valid analog of QG (sPV), that is basedupon the dynamics of PV, is developed for rotating shal-low water on the sphere. Specifically, a PV-streamfunctionrelationship is defined which determines the flow velocitiesfor the entire sphere. At midlatitudes, the fluid dynam-ics are asymptotically equivalent to the beta-plane theoryof QG, in the usual small Rossby number sense. In theequatorial regions, wave propagation at short-scales mim-ics the dispersion relation for equatorial beta waves. GlobalRossby waves, as described in recent works by Verkley(2007) and Schubert (2008), are also included within thesPV framework. As a benchmark test of the dynamics, thepropagation of waves in the sPV model are shown to bean excellent approximation to computations of the equa-torial crossing of topographic waves by Grose & Hoskins(1979). Despite that this sPV model is not obtained in theusual manner of small Rossby number asymptotic analysis,the propagation of mesoscale waves across the equatorialregion retains QG-like accuracy. The mathematical con-

GS11 Abstracts 73

sistency of these sPV dynamics with the rotating shallowwater primitive equations is demonstrated from the per-spective of ray theory. Extensions to baroclinic instabilityand the possibility of PV coupling to Kelvin waves are dis-cussed.

David J. MurakiDepartment of MathematicsSimon Fraser Universitymuraki@math.sfu.ca

MS2

A Simple Model for Atmospheric CirculationsDriven by Convection

This talk proposes a mathematical theory explaining thesharp transition between tropics and extra-tropics in termsof the diurnal cycle of thermal forcing by the sun. Thistransition, at a latitude of 30 degrees, coincides with theouter edge of the Hadley cells, and is marked by a steepjump in the height of the troposphere, from around fifteenkilometers in the tropics to about nine in the mid and highlatitudes. The tropics, equatorwards of 30 degrees, arecharacterized by easterly surface winds -the Trades- and astrong diurnal signal in the wind, pressure and tempera-ture, often marked by regular daily storms in the rainy sea-son. Polewards of 30 degrees, the winds are westerly, andthe weather systems have longer spatio-temporal scales.This change of behavior can be explained in terms of di-urnal waves, created by thermal forcing and trapped equa-torwards of 30 degrees by the Coriolis effect [?]. Thesewaves organize the convective activity, leading to more ac-tive mixing and vertical transport in the tropics. This canbe illustrated in simple mathematical models, presentlyranging from forced linear oscillators to nonlinear conserva-tion laws with entraining shock waves, accounting for theentrainment into the troposphere of air from the surfaceboundary layer.

Esteban G. TabakCourant InstituteNew York Universitybtabak@cims.nyu.edu

MS3

Seismic Imaging of Teleseismic Waves using Gaus-sian Beams

The earthquake seismology community now regularly usesseismic waves from distant sources to illuminate structuresbeneath seismic arrays in so-called passive imaging exper-iments. Similarly, oil reservoirs for petroleum applicationscan be imaged with seismic waves incident from belowusing sources in boreholes. Gaussian beams can be ap-plied for passive imaging based on an over-complete frame-based Gaussian beam representation of the seismic wave-field. Paraxial Gaussian beams are then utilized for thepropagation of the seismic waves back into the medium.The approach provides stable imaging of seismic data insmoothly varying background media where caustics andtriplicated arrivals can exist. Gaussian beam imaging isfound to be very flexible with respect to different experi-mental geometries and can be configured to allow for dif-ferent types of converted or reflected waves. A syntheticexample is first given for a collisional zone structure withan incident P-wave from below where several different scat-tered wave types are used to image the structure. Seismicdata from the 1993 Cascadia experiment are then used toimage the subduction zone beneath the Pacific Northwest

in Oregon. Finally, Gaussian beam migration of seismicdata from the recent Hi-CLIMB experiment in Tibet isused to image the Tibetan lithosphere. The results fromGaussian beam imaging are found to compare favorablywith imaging results obtained using ray/Born inversion.

Robert NowackPurdue Universitynowack@purdue.edu

MS3

Gaussian Beam Methods

Gaussian beams and their superpositions are approximatehigh frequency solutions to linear hyperbolic PDEs. In thistalk, I will give a brief review of Gaussian beams and theirsuperpositions and discuss some of the mathematical toolsthat are necessary to prove that they are valid asymptoticsolutions. From a simulation point of view, I will addressthe question of how to decompose high frequency initialand boundary data into a superposition of Gaussian beams.

Nicolay TanushevDepartment of MathematicsThe University of Texas at Austinnicktan@math.utexas.edu

MS3

The Basics of Constructing Frames Entirely out ofComplex Gaussians and Applications to the WaveEquation

We focus on the construction of a frame of complex Gaus-sians for the space of L2(Rn) functions. When propa-gated along bicharacteristics for the wave equation, theframe can be used to build a parametrix with suitable er-ror terms. When the coefficients of the wave equation havemore regularity, propagated frame functions become Gaus-sian beams. This work is theoretical in nature and relatesto the errors in Gaussian beam solutions.

Alden WatersUCLAamswaters@math.ucla.edu

MS3

Frozen Gaussian Approximation for High Fre-quency Wave Propagation

The frozen Gaussian approximation provides a highly effi-cient computational method for high frequency wave prop-agation. It makes use of fixed-width Gaussian functionson phase plane to approximate the solution. The moti-vation comes from Herman-Kluk propagator developed inchemistry literature. The method works in both scenarioof caustics and spreading. Lagrangian and Eulerian algo-rithms will be introduced in this talk. Rigorous analysisresult on the convergence of this method will be also pre-sented.

Xu Yang, Jianfeng LuCourant Institute of Mathematical SciencesNew York Universityxuyang@cims.nyu.edu, jianfeng@cims.nyu.edu

MS4

Hybrid Simulations of Reactive Transport in

74 GS11 Abstracts

Porous Media

Darcy-scale models of flow and transport in porous mediaoften fail to describe experimentally observed phenomena,while their pore-scale counterparts are accurate but can becomputationally prohibitive. Most numerical multi-scalemodels, which seek to combine these two descriptions, re-quire empirical closures and/or assumptions on the behav-ior of pore-scale quantities at the continuum (Darcy) scale.We present a general formulation of an iterative hybridnumerical method that links these two scales without re-sorting to such approximations. The algorithm treats thefluxes exchanged at the internal boundaries between thepore- and continuum-scale domains as unknown, and al-lows for iteratively determined boundary conditions to beapplied at the pore-scale in order to guarantee their con-tinuity. While the algorithm proposed is general, we useit to model Taylor dispersion in a fracture with chemicallyreactive walls. Results show significant improvement uponstandard continuum-scale formulations.

Ilenia BattiatoMax Planck Institute for Dynamics and Self-Organizationilenia.battiato@ds.mpg.de

Daniel M. TartakovskyUniversity of California, San Diegodmt@ucsd.edu

Alexandre TartakovskyPacific Northwest National Laboratoryalexandre.tartakovsky@pnl.gov

MS4

Influence of THMC Couplings on Thermal Recov-ery from EGS Systems

We explore the evolution of thermal output from EGSreservoirs where coupled THMC effects influence the evolu-tion of permeability structure and respond to the presenceof heterogeneity at a variety of length-scales. Heterogene-ity results from the presence and initial length, orientationand strength of fractures present within the reservoir andthe response is exacerbated by the strong coupling betweenTHMC processes.

Joshua TaronUFZjoshua.taron@ufz.de

Derek ElsworthPenn State Universityelsworth@psu.edu

Ghazal Izadi, Baisheng ZhengEnergy and Mineral EngineeringPenn State Universitygui2@psu.edu, bzz105@psu.edu

MS4

Uncertainty Quantification in Stochastic DiscreteFracture Network THMC Model

Fractures and fracture networks are the principle pathwaysfor migration of water and heat in enhanced geothermalsystems, oil and gas reservoirs migration, carbon diox-ide leakage from carbon sequestration field, and radioac-tive and toxic industrial wastes from underground storagerepositories. A stochastic discrete fracture network and a

HTMC coupling will be presented. Using Monte Carlo sim-ulations, we present the impact of parameter uncertaintiesof the geological characterization on the response of theHTMC model.

Souheil M. EzzedineLLNLezzedine1@llnl.gov

MS4

Hydromechanical Simulation of Triggered Earth-quakes and Mine Dewatering

Two hydromechanical simulations are presented. (1) Insouth Iceland two magnitude Ms 6.6 earthquakes in June2000 were separated by an 81-hour time delay and 18-kmdistance. The models test the hypothesis that the pairingis the result of a two-step triggering process. (2) In theformer Homestake gold mine in Lead, S.D., smulations wereable to explain the co-existence of shallow and deep flowsystems, which are characterized by significantly differenthydromechanical properties.

Herbert WangUniversity of Wisconsinwang@geology.wisc.edu

K. L. Feigl, T AliU. of Wisconsin-Madisonfeigl@geology.wisc.edu, ali@geology.wisc.edu

L.C. MurdochClemson Univmudodc@clemson.edu

MS5

Adaptive Pattern Research for Parallel Block Ap-proximate Inverses

An adaptive algorithm is presented to generate automat-ically the non-zero pattern of the Block FSAI (BFSAI)preconditioner. It is demonstrated that in SPD problemsBFSAI minimizes an upper bound of the Kaporin numberof the preconditioned matrix. The mathematical structureof this bound suggests an efficient parallel strategy to im-prove a given non-zero pattern of BFSAI, providing a novelAdaptive BFSAI (ABF) preconditioner. Numerical exper-iments performed on large FE matrices provide evidence ofABF effectiveness.

Carlo JannaDMMMSA - University of Padovajanna@dmsa.unipd.it

Massimiliano FerronatoUniversity of PadovaDMMMSAferronat@dmsa.unipd.it

MS5

Block Preconditioners for Fully Implicit Atmo-spheric Climate Simulations

We discuss the development of block preconditioners inan effort to reduce computational costs associated withfully implicit time integration of atmospheric climate mod-els within CAM-HOMME. We construct a fully implicitframework based on the shallow water equations and view

GS11 Abstracts 75

the subsidiary linear system as a block matrix. Formal LUdecomposition is performed and block preconditioners arederived based on approximations to the upper triangularblock.

P. Aaron LottLawrence Livermore National LaboratoryAaron.Lott@llnl.gov

MS5

Preconditioning for Flow and for Flow Control

I will describe some solution techniques for flow compu-tations and for optimization problems for the control offlows. In particular, I will describe preconditioned iterativesolution methods for incompressible viscous flow (Stokesand Navier-Stokes problems) and for problems of PDE-constrained optimization where incompressible flow equa-tions provide the constraints. These approaches are appli-cable to finite element and other discretization methods.

Andrew J WathenOxford UniversityNumerical Analysis Groupwathen@maths.ox.ac.uk

MS5

An Accelerated Fixed-Point Iteration for Solutionof Variably Saturated Flow

We investigate effectiveness of an acceleration method ap-plied to the modified Picard iteration for simulations ofvariably saturated flow. We solve nonlinear systems usingboth unaccelerated and accelerated modified Picard itera-tion as well as Newton’s method. Since Picard iterationscan be slow to converge, the advantage of acceleration is toprovide faster convergence while maintaining advantages ofthe Picard method over the Newton method. Results indi-cate that the accelerated method provides a robust solverwith significant potential computational advantages.

Homer F. WalkerWorcester Polytechnic Institutewalker@wpi.edu

Carol S. WoodwardLawrence Livermore National LaboratoryCenter for Applied Scientific Computingcswoodward@llnl.gov

Ulrike YangLawrence Livermore National Laboratoryumyang@llnl.gov

MS6

Macroscale Potentials for Charged Swelling PorousMedia

In this talk we discuss the macroscopic potentials thatinduce bulk fluid flow or diffusive flow through swellingporous materials. Swelling porous media such as expan-sive soils, food stuff, biotissue, and swelling polymers havecomplex microstructure such as a possibly charged solidsurface and a large liquid-solid interface causing the solidand liquid to be highly interactive. Here we discuss themacroscopic pressures and chemical potentials that pro-

duce flow within the framework of hybrid mixture.

Lynn S. BennethumUniversity of Colorado DenverLynn.Bennethum@cudenver.edu

MS6

A Two-Scale Computational Model of pH-SensitiveSwelling Porous Media

In this talk we present the pore-scale modeling of a porousmedium composed of electrically charged macromoleculessaturated by an electrolyte solution with four ionic mono-valent species (Na+,CL-,H+,OH-). Ion exchange reactionsgive rise to a pH-dependent surface charge which is mod-eled by a nonlinear Neumann boundary condition for thePoisson-Boltzmann governing the local electric potential.By coupling the governing equations in the fluid domainwith the elasticity problem for the solid particles the ho-mogenization procedure is applied to upscale the modelto the macroscale. Among the homogenized results a newconstituive law is derived for the disjoining pressure de-pendent on pH. Numerical simulations of a free swellingexperiment are performed and results compared with ex-perimental observations.

Marcio A. MuradNational Laboratory of Scientific ComputationLNCC/MCTmurad@lncc.br

Ranena PonceDept Engineering Mechanics PUC/RJponcerv@puc-rio.br

Sidarta LimaFederal University Rural of Rio deJaneirosidarta@lncc.br

MS6

The Impact of Pore Deformation on Sorption andCapillary Condensation in Mesoporous Solids

We report recent theoretical developments in the study ofgas-liquid transitions of fluids confined to deformable meso-porous materials. Due to a synergistic coupling the phasebehavior of the confined soft matter phase is significantlyaffected by the deformation of the confining material whichin turn is deformed as a result of phase changes occur-ring in the confined phase. If the confined fluid is gas-likeits wetting characteristics affect the deformation isothermsuch that the pore may expand or contract as more gas isadsorbed prior to capillary condensation. Directly at cap-illary condensation the pore abruptly shrinks on accountof fluid-substrate attraction. If the density of the confinedliquid-like phase is then enhanced further the pore expandsagain. This expansion allows one to determine nanome-chanical properties of the confining solid directly from thedeformation isotherm. In the future it might be possibleto fabricate sensors that allow one to measure mechani-cally changes in thermodynamic properties of confined softmatter phases.

Martin SchoenStranski Laboratorium fur Physikalische und Theor.ChemieTechnische Universitat Berlinmartin.schoen@fluids.tu-berlin.de

76 GS11 Abstracts

MS6

Food Engineering Applications of Continuum Me-chanics

During fluid transport processes such as drying, sorptionand frying, physical and chemical changes take place in thefood biopolymers. Hybrid mixture theory based multiscaleequations were developed that allow incorporating thesechanges into transport models. Multiscale transport andthermomechanical equations were solved to predict fluidtransport (vapor, water, oil) and viscoelastic stresses infoods. Comparisons were made to the macro and micro-scale experiments. The optimized operating parametersresulting in improved food quality were obtained.

Pawan S. TakharAnimal and Food SciencesTexas Tech Universitypawan.takhar@ttu.edu

MS7

Upscaling Kinetics and Geometrical Heterogeneityfor Flow and Transport Models

The transport of dissolved species in porous media is amajor concern for the environment, for waste storage man-agement, agriculture or carboxyde underground storage.Anomalous diffusion is frequently observed within the con-text of natural porous media, especially in the under-ground. We aim to focus on different meanings of the word”anomalous”. We revisit the classical problem of disper-sion of a point discharge of tracer in laminar pipe Poiseuilleflow. For Peclet numbers corresponding to Taylor’s disper-sion regime, we derive rigorously an effective model for theenhanced diffusion. It is justified by error estimates. Weexplicit the retardation and memory effects of the adsorp-tion/desorption reactions on the dispersive characteristicsand show their importance. The chemistry influences di-rectly the characteristic diffusion width and the effectiveconvection. Then we show how tracer dispersion can bedivided into three regimes. For small times, diffusion dom-inates advection yielding a symmetric Gaussian dispersioncloud. At large times, the flow is in the Taylor regime.However, in an intermediate regime, the longitudinal diffu-sion is anomalous. We emphasize that the previous effectis completely different from the nonfickian effects often ob-served before the diffusive asymptotic. An example involv-ing fractional derivatives is rigorously constructed throughrandom walks.

Catherine ChoquetUniversity of Marseillec.choquet@univ-cezanne.fr

MS7

Upscaling of Reactive Flows Involving Free Bound-aries

We consider the transport of solute particles in a reac-tive flow under dominant transport conditions for the vari-able geometry in the case of a thin strip. We derive theupscaled model(1-D) from the 2-D model using perturba-tion methods and compare the 1-D model with direct 2-Dcomputations numerically. Further, we use rigorous ho-mogenization techniques for a specific choice of reactionrate, namely crystal precipitation and dissolution in peri-odic porous medium (fixed geometry case).

Kundan Kumar

Technische Universiteit Eindhoven, Netherlandsk.kumar@tue.nl

MS7

Upscaling of Adsorptive Transport Under Unsatu-rated Condition

In general, solute transport mechanisms under saturatedconditions have been studied in detail. However, under un-saturated conditions, these mechanisms need to be under-stood in greater detail. In such cases, dispersion coefficientvaries with Darcy velocity and saturation, and principal in-teractions usually occur at the solid-water interfaces (SWI)and air-water interfaces (AWI), thus greatly influenced bywater content. In this study, we have investigated upscal-ing of adsorptive transport process under unsaturated con-ditions.

Amir RaoofUniversity of Utrecht, Netherlandsraoof@geo.uu.nl

Majid HassanizadehUniversity of Utrechthassanizadeh@geo.uu.nl

MS7

Upscaling in-situ Combustion Processes for HeavyOil Recovery When Kinetics and Phase BehaviorWreak Havoc

In-situ combustion is an attractive enhanced recoverymethod for heavy oil reservoirs: a small fraction of the oilis burned in-situ, which creates a steam drive and mobilizesthe oil. Traditional reservoir simulators are not capable ofresolving the thin reaction fronts, because these are ordersof magnitude smaller than the typical reservoir scale. In-stead, we propose an upscaled model that effectively rep-resents the heat generation and combustion products atrealistic grid cell sizes.

M GerritsenStanfordmargot.gerritsen@stanford.edu

Zhouyuan Zhu, Alexandre LapeneEnergy Resources Engineering, Stanford.zhuzy@stanford.edu, alexandre.lapene@stanford.edu

MS8

Reduced-Order Models for Boussinesq Flows

We consider POD-Galerkin models for Boussinesq flows.Reduced-bases are computed by post-processing multipleCFD simulations computed using different boundary con-dition inputs. The resulting model allows for time-varyingboundary conditions and seeks to accurately predict thetemperature in a comfort zone in a thermally stratifiedroom. These models are developed to model thermal trans-port in buildings and design the control systems (con-trollers as well as sensor/actuator placement).

Jeff BorggaardVirginia TechDepartment of Mathematicsjborggaard@vt.edu

GS11 Abstracts 77

MS8

New Methods for Estimating Poleward Eddy HeatTransport using Satellite Altimetry

Current-generation altimetry products are too coarse toresolve most of the turbulent spectrum of the ocean anddrastically underestimate eddy fluxes such as the polewardheat transport. We show that, by extracting aliased high-wavenumber information from the low-wavenumber band,one can derive “superresolved’ velocity fields from sparsesatellite observations. When used in combination with anadaptive stochastic model for the unresolved scales, thesetechniques produce significantly better estimates of pole-ward eddy heat transport.

Shane R. KeatingNew York UniversityCourant Institute of Mathematical Sciencesskeating@cims.nyu.edu

MS8

The Two-dimensional Boussinesq System - Analyt-ical and Computational Study

Abstract not available at time of publication.

Adam LariosDepartment of MathematicsUC Irvinealarios@math.uci.edu

MS8

Poisson Solvers in Thin Domains

Abstract not available at time of publication.

Alberto ScottiUNC Chapel Hilltba@amath.unc.edu

MS9

Quantifying Uncertainty in Wind Power Predic-tions for Stochastic Unit Commitment Optimiza-tion

We discuss uncertainty quantification in wind power fore-casts using numerical weather prediction (NWP) modelswith applications in proactive management of energy sys-tems. Weather is one of the major drivers of energy gen-eration and consumption, especially with the adoption ofsuch renewable resources as wind. Our strategy consists inusing numerical dynamical models to forecast ambient con-ditions and propagate uncertainties from initial conditionsto produce accurate confidence intervals. We analyze theimpact of assimilating satellite radiance in our forecasts.We present an integrative unit commitment or energy sys-tem scheduling problem that uses weather forecasts withuncertainty, and validate our results using real observa-tions.

Emil M. ConstantinescuArgonne National LaboratoryMathematics and Computer Science Divisionemconsta@mcs.anl.gov

Victor ZavalaArgonne National Laboratoryvzavala@mcs.anl.gov

Mihai AnitescuArgonne National LaboratoryMathematics and Computer Science Divisionanitescu@mcs.anl.gov

MS9

Data Assimilation System Diagnosis and Tuning ofError Covariance Parameters

The specification of accurate statistical information on theerrors in the prior state estimate and observational datais unanimously recognized as a major practical difficultyin geophysical data assimilation. A mathematical formal-ism to adjoint sensitivity analysis for diagnostics and tun-ing of the error covariance input parameters is provided inthe context of variational data assimilation. Applicationsto atmospheric modeling are presented from the proof-of-concept stage to the current status of implementation atnumerical weather prediction centers.

Dacian N. DaescuPortland State UniversityDepartment of Mathematics and Statisticsdaescu@pdx.edu

MS9

Computational Performance of a Parallel Matrix-free Implementation of the Ensemble Kalman Fil-ter

The Ensemble Kalman Filter (EnKF) has become an im-portant data assimilation tool for numerical models in geo-sciences. For large data sets a potential bottleneck inEnKF is the computation of the Kalman gain matrix. Inthis talk we discuss a matrix-free parallel implementationof EnKF where the form of the matrices is exploited usinga Sherman-Morrison-Woodbury inversion algorithm. Thisapproach scales linearly with the number of observations.Performance results with a shallow-water model are pre-sented.

Humberto C. Godinez, David MoultonLos Alamos National LaboratoryApplied Mathematics and Plasma Physicshgodinez@lanl.gov, moulton@lanl.gov

MS9

Comparison of Ensemble Data Assimilation Meth-ods in the Presence of a Nonlinear Observation Op-erator

A new comparison of three frequently used sequentialdata assimilation methods illuminating their strengths andweaknesses in presence of linear and nonlinear observa-tion operators is presented. The ensemble Kalman filter(EnKF), the particle filter (PF) and the Maximum Likeli-hood Ensemble Filter (MLEF) methods were implementedand spectral shallow water equations model in spherical ge-ometry model was employed using Rossby-Haurwitz Waveno 4 as initial conditions. Numerical tests reveal that allthree methods perform satisfactory for linear observationoperator 15 days model integration, whereas EnKF, withthe nonlinear observation operator failed. The particle fil-ter and the hybrid filter (MLEF) both performed satisfac-torily with highly nonlinear observation operators .

Milija ZupanskiCooperative Institute for Research in the AtmosphereColorado State University

78 GS11 Abstracts

ZupanskiM@cira.colostate.edu

Ionel M. NavonFlorida State UniversityDepartment of Scientific Computinginavon@fsu.edu

Mohamed JardakCSIT, Florida State Universityjardak@csit.fsu.edu

MS10

Amplitude Calculations for 3-D Gaussian BeamMigration using Complex-valued Traveltimes

The use of Gaussian beams to represent Green’s functionsin 3-D Kirchhoff migration algorithms adds four additionalintegrals to the processing. Ross Hill reduced the four inte-grals to two via the method of steepest descent for integralswith complex exponents. He presented the travel time ad-justment, but not the amplitude adjustment necessary fora “true amplitude’ approximation in the Kirchhoff sense.We provide that adjustment here, using a recently devel-oped iterated method of steepest descent.

Norman BleisteinColorado School of Minesnormblei@gmail.com

Samuel H. GrayCGGVeritasCalgary, Canadasam.gray@cggveritas.com

MS10

Seismic Imaging with Gaussian Wave Packets

Fast algorithm for a reverse-time migration of seismic datacan be designed using a flow-out of Gaussian wave packets(GWPs). It consist of three main steps: data decompo-sition into GWPs; their flow-out into subsurface; imagingcondition (cross-correlation of ’source’ and ’receiver’ fields).We achieve sparse data representation with GWPs us-ing iterative non-linear algorithm based on l1-optimizationideas. Rigid GWP flow-out along rays is used for down-ward data continuation. Analytic formulas can be usedfor cross-correlating GWPs after their flow-out (fast im-plementation of the imaging condition).

Anton A. DuchkovIPGGduchkovaa@ipgg.nsc.ru

Fredrik AnderssonLund Universityfa@maths.lth.se

MS10

Improving Wave-equation Fidelity of GaussianBeams by Solving the Complex Eikonal Equation

Gaussian beams are a well-known wavefield approximation.A more accurate representation can be obtained by solvingthe complex eikonal equation. We propose a constructivealgorithm for solving the complex eikonal equation. Byre-writing the complex traveltime as background real andimaginary parts and their respective perturbations, we ar-rive at an update scheme that aims at solving the complex

eikonal equation iteratively. The initial prior may comefrom the Gaussian beam approximation computed by dy-namic ray tracing. The result embraces complete detailsof the velocity model and therefore can help enhancing ac-curacy of Gaussian-beam migration and other applicationsof Gaussian beams in seismology.

Siwei Li, Sergey FomelUniversity of Texas at Austinllisiw@hotmail.com, sergey.fomel@beg.utexas.edu

Alexander VladimirskyDept. of MathematicsCornell Universityvlad@math.cornell.edu

MS10

Recovery of High Frequency Wave Fields

Gaussian beams are asymptotically valid high frequencysolutions to hyperbolic partial differential equations, con-centrated on a single curve through the physical domain.They can also be extended to some dispersive wave equa-tions, such as the Schroedinger equation. Superpositions ofGaussian beams provide a powerful tool to generate moregeneral high frequency solutions that are not necessarilyconcentrated on a single curve. We are concerned withthe accuracy of Gaussian beam superpositions in terms ofthe wavelength, which was thought a rather difficult prob-lem decades ago. We present a systematic constructionof Gaussian beam superpositions for all strictly hyperbolicand Schroedinger equations subject to highly oscillatoryinitial data, and obtain the optimal error estimates in theappropriate norm dictated by the well-posedness estimate.The obtained results are valid for any number of spatialdimensions and are unaffected by the presence of caustics.This talk presents key ideas and techniques involved in thisnewly developed recovery theory of high frequency wavefields, with materials drawn from recent works with J. Ral-ston (UCLA), and with N. Tanushev (UT-Austin) and O.Runborg (KTH).

Hailiang LiuIowa State UniversityUSAhliu@iastate.edu

MS11

Multilevel Model Reduction Approaches for Flowsin Multiscale Porous Media

In this talk, I will describe multilevel multiscale methodsfor flows in highly heterogeneous media with high contrast.In particular, I will describe multilevel construction of basisfunctions and how they can be used in preconditioning offlow equations.

Juan GalvisTexas AMjugal@impa.br

MS11

A Data-driven Stochastic Multiscale Method forModel Reduction and Uncertainty Quantification

We introduce a data-driven stochastic multiscale methodto solve stochastic PDEs. One important feature of thismethods is to construct a multiscale stochastic basis from

GS11 Abstracts 79

limited samples of the stochastic solutions obtained byMonte Carlo methods. This multiscale method effectivelyreduces the dimensionality of the stochastic PDEs. Asa consequence, we reduce the high dimensional stochasticproblem to a relatively small number of coupled determin-istic PDEs. Some numerical results will be presented todemonstrate the effectiveness of the method.

Thomas HouApplied MathematicsCalifornia Technology Institutehou@acm.caltech.edu

MS11

Use of Reduced-order Models for Improved DataAssimilation within an EnKF Context

Reduced order modeling using trajectory piecewise lin-earization (TPWL) has been shown to achieve dramatic(2-3 order of magnitude) speedup for production optimiza-tion problems. In this work, we extend TPWL methodol-ogy to history matching problems. The TPWL represen-tation is then incorporated into an Ensemble Kalman Fil-ter (EnKF) method. TPWL and EnKF combine well, asthe EnKF ensemble provides a reasonably large and variedtraining set for TPWL. Further, because of the sequentialnature of EnKF, where forecasting is performed over shorttime periods, the use of linearized models is reasonable.The performance of the new methodology on 2D and 3Dexample cases is demonstrated.

Pallav SarmaChevron Energy Technology CompanySan Ramon CApallav@chevron.com

MS11

Toward Effective Multiscale Parameterization ofReservoir Models

A survey of emerging approaches toward reliable reservoirperformance Uncertainty quantification and history match-ing often require a large number of reservoir simulationsthat is often infeasible in practice. At the core of the chal-lenge is the curse of dimensionality. In this talk, we ex-amine the premises of the existing modeling approach andreview recent advances in reservoir characterization, geo-logic modeling, and understanding of impact of geologicfeatures on fluid flow. These advances point to potentialways of effective, multiscale parametrization of reservoirmodels.

Xiao-Hui WuExxonMobil Upstream Research Companyxiao-hui.wu@exxonmobil.com

MS12

Thermo-hydro-mechanical Modeling in Porous Me-dia: A Coupled Mixed and Galerkin Finite ElementFormulation

The efficient solution to the coupled system of PDEs gov-erning the mass and the energy balance in deformableporous media requires advanced numerical algorithms. Acombination of Mixed and Galerkin Finite Elements alongwith a staggered method are employed, addressing iter-atively flow-deformation by a coupled approach and heattransport via a splitting technique, at each time step. Suchformulation warrants stable numerical solutions, element-

wise conservative velocity fields and accurate prediction ofsharp temperature convective fronts.

Nicola CastellettoDMMMSAUniversity of Padovacastel@dmsa.unipd.it

Massimiliano Ferronato, Giuseppe GambolatiUniversity of PadovaDMMMSAferronat@dmsa.unipd.it, gambo@dmsa.unipd.it

MS12

Coupled Poromechanics of Faulted Reservoirs

The coupling between pore pressure and mechanical de-formation is essential to understand the initiation of faultslip and the evolution of fault hydraulic properties. Thiscoupling is likely a critical determinant of when and whereearthquakes are triggered, but the mechanisms controllingthe influence of the pore pressure field on the onset of slipare currently poorly understood. Here, we present a cou-pled model of flow and mechanics of faulted geologic reser-voirs. Faults are represented as 2D entities embedded ina 3D domain, which exhibit irreversible behavior in theirfriction and dilatancy poromechanical response. We em-ploy an unconditionally-stable iteratively coupled schemeto solve the coupled flow-mechanics equations, which weimplement in an open source tectonic deformation simula-tor.

Birendra JhaMITCivil and Environmental Engineeringbjha@mit.edu

Bradford HagerMITEarth, Atmospheric and Planetary Sciencesbrad@chandler.mit.edu

Ruben JuanesMITCivil and Environmental Engineeringjuanes@mit.edu

MS12

Coupling Geomechanics and Multiphase Flow inPorous Media

We discuss Biot models that treat the coupling of mul-tiphase flow and elasticity in different subdomains. Ex-tensions that include compositional flow are also consid-ered. Here we employ locally conservative algorithms suchas mixed finite element methods for flow and Galerkin formechanics. Theoretical error estimates for certain modelproblems will be given as well as computational results.

Mary F. WheelerCenter for Subsurface ModelingUniversity of Texas at Austinmfw@ices.utexas.edu

MS12

Scalable Newton-Krylov Solvers for Coupled Hy-

80 GS11 Abstracts

dromechanical Systems

In this work, we consider efficient solution methods formixed finite element models of fluid flow through de-formable porous media. In many geotechnical and geo-physical applications, the behavior of a solid/fluid mixtureis highly-nonlinear, introducing additional challenges fortightly-coupled solution algorithms. In our talk we focuson the implementation of implicit Newton-Krylov methodsfor coupled hydromechanical problems. The main difficultyis to design effective preconditioners that achieve good al-gorithmic scaling on today’s high performance computingplatforms. We highlight an approach in which precondi-tioners are constructed from block factorizations of thecoupled systems. The resulting methodology allows oneto extend single-physics preconditioners in a natural wayto multiphysics applications, allowing for significant codereuse and an object-oriented framework. We test the per-formance of the proposed techniques on several numericalexamples drawn from geotechnical and reservoir engineer-ing applications.

Ronaldo BorjaStanford Universityborja@stanford.edu

Joshua WhiteLawrence Livermore National Laboratoryjawhite@llnl.gov

MS13

Iterative Solution Methods for Stokesian Dynamics

Stokesian dynamics is a computational technique for simu-lating the motions of particles suspended or dispersed in afluid medium and interacting through hydrodynamic andnon-hydrodynamic forces. Particle velocities are computedfrom the forces by solving with a resistance matrix which isa function of particle positions and orientations only. Theresistance matrix is composed of a slowly-changing, dense,long-range component, plus a fast-changing, sparse, indefi-nite, short-range component. We discuss iterative solutionmethods for scaling up Stokesian dynamics to very-largeproblem sizes by exploiting this structure of the resistancematrix, as well as the design of preconditioners suitablefor upcoming high-performance computing architectures.Joint work with Tadashi Ando and Jeffrey Skolnick.

Edmond ChowSchool of Computational Science and EngineeringGeorgia Institute of Technologyechow@cc.gatech.edu

MS13

Constraint Preconditioners for Ill-conditionedConsolidation Problems

Block constraint preconditioners prove very efficient forthe solution of the indefinite linear systems arising in FEconsolidation problems. Their implementation on parallelcomputers, however, is not straightforward. We present anovel Parallel Inexact Constraint Preconditioner (ParICP)which is based on Block FSAI, a recent and promising de-velopment in the field of approximate inverses. ParICP isa scalable and efficient implementation of constraint pre-conditioning for high performance computing, proving veryrobust especially in ill-conditioned problems.

Massimiliano Ferronato

University of PadovaDMMMSAferronat@dmsa.unipd.it

Carlo JannaDMMMSA - University of Padovajanna@dmsa.unipd.it

Giuseppe GambolatiUniversity of PadovaDMMMSAgambo@dmsa.unipd.it

MS13

Preconditioning Surface and Subsurface Flow Cou-pling for Arbitrary Geometries on a StructuredGrid

Due to complex dynamics inherent in the physical mod-els, numerical formulation of subsurface and overland flowcoupling can be challenging to solve. ParFlow is a sub-surface flow code that couples with overland flow via anoverland boundary condition prescribed at the top surface.This talk will present a preconditioning approach to dis-crete systems arising from implicit coupling of these flowregimes in ParFlow. Numerical results will explore the ef-fectiveness of the preconditioner and its cost.

Daniel Osei-KuffuorUniver. of Minnesotadosei@cs.umn.edu

Reed M. MaxwellDepartment of Geology and Geologic EngineeringColorado School of Minesrmaxwell@mines.edu

Steve G. Smith, Andy Tompson, Carol S. WoodwardLawrence Livermore National Labsmith84@llnl.gov, tompson1@llnl.gov,woodward6@llnl.gov

MS13

Quasi-Newton Preconditioner Updates for Two-phase Flow Simulations

We study Broyden-type rank-one updates of an initialpreconditioner for solving the sequence of linear systemsarising from Newton-like linearizations of FEM-discretizedtwo-phase flow problems. Starting from the incomplete LUdecomposition of the initial Jacobian matrix, we apply thisapproach to build a sequence of preconditioners. Numericalexperiments show a reduction in the number of iterationsneeded to achieve convergence in the linear solver and inthe cost of computing the preconditioner.

Luca BergamaschiUniversita di PadovaItalyberga@dmsa.unipd.it

Mario PuttiDept. Mathematical Methods and Models for AppliedSciencesUniversity of Paduaputti@dmsa.unipd.it

GS11 Abstracts 81

MS14

Evaporative Deposition Patterns of Bacteria andMicrospheres from a Sessile Drop: Potential forCharacterizing Particle Adhesiveness

Evaporative deposition of colloidal particles (bacteria andmicrospheres) on mica from a sessile drop is investigated asa simple way to control particle deposition as well as inves-tigate fundamental particle-surface forces. We show thatit is possible to continuously vary the deposition patternfrom ring deposits to cellular pattern deposits by incre-mental changes in surface wettability which we achieve bytimed exposure of the mica surface to the atmosphere.

Joan CurrySoil, Water and Environmental ScienceUniversity of Arizonacurry@ag.arizona.edu

MS14

Heterogeneous Reactions with Memory and Linksto Multirate Mass Transfer Models of ConvolutionType

The convolution form used to express mass transfer be-tween mobile and immobile aqueous domains, and oftenassociated with multirate mass transfer representations ofmatrix diffusion processes, is generalized to the case of un-equal forward and reverse rates for each of the multiplerates of the multirate mass transfer, and is shown to rep-resent also linear but non-Markovian reactions that kinet-ically partition mass between mobile and immobile phaseswith rate of return to mobile phase dependent on contigu-ous time spent in immobile phase. In the case where amultirate model refers to multiple sites with distributedmobilization or release rates but single-valued immobiliza-tion rate, an equivalent formulation is found using singlesite mobilization-immobilization with non-Markovian mo-biliation rate dependent on contiguous time spent immo-bilized.

Tim GinnUniversity of California at Davistrginn@ucdavis.edu

MS14

Fractional Brownian Motion Run with a Non-linearClock

We construct a family of stochastic processes with nonsta-tionary, correlated increments which allow a priori indepen-dent selections of both fractal dimension and mean-squaredisplacement. The family is essentially fractional Brown-ian motion (fBm) run with a non-linear clock (fBm-nlc).The fractal dimension of fBm-nlc is shown to be the sameas that of the underlying fBm process. We also computethe p- variation and discuss the problems in using this todifferentiate between diffusive processes.

Dan O’MalleyPurdue Universityomalled@purdue.edu

MS14

Upscaling Chaotic Dynamics in Porous Media viaCentral Limit Theorems

There are several upscaling (renormalization) techniquesfor transport in porous media. All approaches in Statis-

tical Mechanics except the upscaling tool via central limittheorems (CLT) use second moments. When Levy motionsare applied to velocity or position processes CLT plays sig-nificant roles in modeling transport in porous media. Inthis talk, I will present the results in the CLT approach formicrobial motility in porous media.

Moongyu ParkUniversity of Alabama at HuntsvilleDepartment of Mathematicsmp0002@uah.edu

MS15

Homogenization of the Linearized Ionic TransportEquations in Rigid Periodic Porous Media

We undertake the rigorous homogenization of a systemof PDEs describing the transport of a N-component elec-trolyte in a dilute solvent through a rigid porous medium.Smallness of the electric field and hydrodynamic force, al-lows us using O’Brien’s linearized equations as the start-ing model. We establish convergence of the homogeniza-tion procedure and prove that Onsager’s effective tensor issymmetric positive definite. (Joint work with G. Allaire(Paris) and A. Piatnitski (Narvik))

Andro MikelicInstitut Camille Jordan, Departement de MathematiquesUniversite Lyon 1Andro.Mikelic@univ-lyon1.fr

MS15

Homogenization of a Sulfate Corrosion Problem:Modelling and Analysis

We model and then analyse a reaction-diffusion (RD) sce-nario describing the agressive corrosion with sulfates of thesewer pipes made of concrete. Besides being partly dissipa-tive, our RD system includes two interface-reaction mech-anisms: (1) the Henry’s law and (2) a non-linear chemicalreaction capturing the action of the most aggressive species– SO2−

4 – on the boundary of the pore walls. After dis-cussing basic aspects of the pore-model analysis, we focuson the rigorous derivation of a set of macroscopic equa-tions. As periodic homogenization limiting procedure, weuse the two-scale convergence approach combined with theperiodic unfolding. The main difficulty lies in passing tothe (homogenization) limit in the nonlinear reaction termsdefined on the oscillatory micro-interfaces. We derive boththe weak and strong formulation of the limiting RD system.We conclude the talk by pointing out correctors, which de-fine the quality of our averaging procedure.

Adrian MunteanDepartment of Mathematics and Computer ScienceTU Eindhovena.muntean@tue.nl

Tasnim FatimaDepartment of Mathematics and Computer ScienceTU Eindhoven, NLt.fatima@tue.nl

MS15

Colloid and Fluid Dynamics in Porous Media -Modelling, Analysis and Numerics

We consider a non-stationary electro-hydrodynamic sys-

82 GS11 Abstracts

tem at the pore scale. After applying homogenizationtechnique to this system of partial differential equationswe discuss the resulting equivalent macroscopic model de-scription. These theoretical results are complemented bynumerical simulations. As special application we therebyfocus on colloidal transport within a porous medium, whichfundamentally influences contaminant transport. Exten-sions of the model regarding changes of the underlying mi-crostructure due to interaction with the porous matrix willalso be considered.

Nadja RayUniversity of Erlangen-Nurembergray@am.uni-erlangen.de

Florian FrankFriedrich-Schiller University of Jenafrank@am.uni-erlangen.de

MS15

Moving Boundary Problems in Porous Media

We discuss processes in porous media with moving bound-aries at the pore-scale such as deposition, biofilm growthand crystal dissolution and precipitation. All these pro-cesses may change the pore geometry. We use the pore-scale free boundary problem to derive upscaled effectiveequations on the Darcy scale via a formal homogenizationprocedure. Numerical simulations show that solutions ofthe upscaled model match the averaged solutions of thepore-scale model very well.

T. L. van NoordenEindhoven University of Technologyt.l.v.noorden@tue.nl

MS16

A Predictive Pore-Scale Model for Non-Darcy Flowin Porous Media

Non-Darcy flow is porous media often observed in domainswhere relatively high velocities occur. In these regions anempirical model, Forchheimers equation, is used. In thisstudy, we use the method of homogenization to develop afiltration law in porous media that includes the effects ofinertia at finite Reynolds numbers. A major contribution ofthis study is that the coefficients of the polynomial law canbe derived a priori, by solving sequential Stokes problems.

Matthew BalhoffICESThe University of Texas at Austinbalhoff@ices.utexas.edu

MS16

Modeling of Well Productivity Index for NonlinearFlows and Applications in Reservoir Engineering

Motivated by the concept of the well Productivity Index(PI) we study a functional for general non-linear Forch-heimer equation. The impact of the nonlinearity on thevalue of the PI is analyzed. Exact formula for the “skinfactor’ in radial case is derived. Dynamics of the PI for theclass of boundary conditions is studied. Developed frame-work is applied to obtain non-linear analog of Peacemanformula for the well-block pressure in unstructured grid.

Lidia Bloshanskaya

Texas Tech UniversityDepartment of Mathematics and Statisticslidia.bloshanskaya@ttu.edu

Eugenio AulisaDepartment of Mathematics and Statistics.Texas Tech Universityeugenio.aulisa@ttu.edu

MS16

On Non-Darcy Flows in the Porous Media

Non-Darcy flow is usually treated by approximate analyt-ical and numerical techniques in petroleum engineering.Recent applications in gas reservoirs, hydraulic fractures,and naturally fractured porous media, however, requiremore detailed treatments. Of particular interest are thepressure- and rate-transient responses of wells under theinfluence of non-Darcy flow. This talk will summarize thestandard treatment of non-Darcy flow in petroleum engi-neering and discuss the approximate application of decon-volution for non-Darcy flow.

Erdal OzkanColorado school of mines petroleum engineeringeozkan@exchange.mines.edu

MS16

Modeling Flow with Inertia at Porescale andMesoscale: Implications for Transport

We discuss computations of flow at pore-scale andmesoscale via discretizations of Navier-Stokes and non-Darcy models. We upscale from pore-scale for linear lami-nar and inertia regimes of Reynolds numbers and comparewith experimental data. We address the issues of grid-convergence and appropriate scaling needed when REVand grain size change, as in homogenization. Most recentresults concern the influence of inertia models on the pa-rameters of transport coupled to the flow at pore-scale andmesoscale.

Anna TrykozkoUniversity of Warsawaniat@icm.edu.pl

Malgo PeszynskaDepartment of MathematicsOregon State Universitympesz@math.oregonstate.edu

Ken KennedyOregon State Universitykennedke@math.oregonstate.edu

MS17

UTBEST3D – A Coastal Ocean Modeling SystemBased on a Discontinuous Galerkin Method

We describe the application of a Local DiscontinuousGalerkin method to the three-dimensional hydrostatic sys-tem in primitive variables for coastal and ocean modeling.Starting from a simple ’proof-of-concept’ code UTBEST3Dgrew into a modular, object-oriented, highly scalable par-allelized package that can be used to simulate barotropicand baroclinic turbulent flows for a wide range of physical

GS11 Abstracts 83

conditions and forcings.

Vadym AizingerMax Planck Institute for Meteorologyvadym.aizinger@zmaw.de

Clint DawsonInstitute for Computational Engineering and SciencesUniversity of Texas at Austinclint@ices.utexas.edu

MS17

Issues in Coastal Ocean Modeling

In this talk we will give an overview of current issues incoastal ocean modeling that will be discussed by variousspeakers in this minisymposium. We will also discuss re-cent research on hurricane storm surge modeling and theapplication of discontinuous Galerkin methods to modelingflow and transport processes in the near shore.

Clint DawsonInstitute for Computational Engineering and SciencesUniversity of Texas at Austinclint@ices.utexas.edu

MS17

A Triangular Discontinuous Galerkin CoastalOcean Model (dgcom)

We will report on current and future developments of DG-COM which is a research code for simulating tsunamis andstorm surges. In this talk we will report on the inclusionof high-order time-integrators including their implementa-tion with boundary conditions (no-flux, non-reflecting, andwetting and drying conditions). Finally, we will describeour plans to include adaptivity into the triangular codefor tracking storm-surges. Time permitting, we will de-scribe the DG non-hydrostatic atmospheric model that isalso under development that will be used to generate thewind stresses to be used in storm-surge simulations. Theoverlap between the two models will be discussed as wellas the MPI implementation of the DG amtospheric modeland strategies for coupling the two models.

Shivasubramania GopalakrishnanDepartment of Applied MathematicsNaval Postgraduate Schoolsgopalak@nps.edu

Francis X. GiraldoNaval Postgraduate Schoolfxgirald@nps.edu

MS17

Quantifying Uncertainty in HYCOM simulation ofthe Gulf of Mexico

Oceanic simulations have numerous input parameters thatare either unknowns, obtained from calibration, or knownonly approximately. These include, for example, initialand boundary conditions, as well as parameter embeddedwithin subgrid scale parametrization. These uncertaintieslead naturally to uncertainties in the output parameters;parametric studies must then be performed to explore thedependency of the solution on these parameters. Here weexplore one approach to uncertainty quantification usingpolynomial chaos expansions, and apply the methodology

to Gulf of Mexico simulations using the Hybrid Coordi-nate Ocean Model. Examples of uncertainty outputs willbe be presented, and the potential and limitations of themethodology will be presented.

Mohamed IskandaraniRosenstiel School of Marine and Atmospheric SciencesUniversity of MiamiMIskandarani@rsmas.miami.edu

Ashwanth SrinivasanUniversity of Miamiashwanth@rsmas.miami.edu

Carlisle ThackerNational Oceanic and Atmospheric Administrationcarlisle.thacker@noaa.gov

Omar M. KnioDept. of Mech. Eng.Johns Hopkins Universityknio@jhu.edu

MS18

Variational Data Assimilation for Fine-scale CO2Source/Sink Estimation

Measurements of atmospheric CO2 concentration are be-coming available at increasingly dense spatial and temporalresolution, most notably from satellites such as GOSAT,the OCO reflight mission, and other planned missions. Ifsuccessful, these data could permit estimation of sourcesand sinks of CO2 at scales of 100-200 km or better, at sub-synoptic time resolutions. While these data will initiallypermit only net CO2 sources to be estimated, separationof the anthropogenic and natural components may also be-come easier using measurements of other species, such asC14, NOx, etc. Estimating surface CO2 fluxes at atmo-spheric model grid resolution imposes computational de-mands that are being met with methods that achieve theirefficiency by abandoning the calculation of the full-rankcovariance of the estimate. Here we present one of thesemethods, variational data assimilation, as applied to thesurface source/sink problem. We will discuss the physicalaspects of the problem, including the linearity of atmo-spheric transport (no internal chemical sinks) for CO2, aswell as the time scales of atmospheric mixing, and their im-plications for any estimation system. We will outline thethe method, including a description of the control variablestrategy used. We will discuss the calculation of the low-rank covariance estimate, computed here using the BFGSmethod. And we will give some representative results fromsimulation studies.

David F. BakerCooperative Institute for Research in the Atmospheredfbaker66@gmail.com

MS18

A Geostatistical Ensemble Square-Root Filter forEstimating Surface Fluxes of CO2

In recent years, one of the important challenges that hasemerged in CO2 source/sink estimation is the increasein computational cost associated with solving the atmo-spheric inverse problem. Solving problems in batch mode isbecoming more and more computationally infeasible giventhe increasing spatial and temporal resolution of satellitedata and ground based CO2 concentration measurements.

84 GS11 Abstracts

The alternative to these batch approaches are data as-similation (DA) techniques that efficiently solve the in-verse problem by making certain numerical approxima-tions. However, a fundamental question that has remainedunanswered is the impact on estimation precision and ac-curacy by implementing the numerical DA tools relative tobatch inversions. In this work, we will present the first re-sults from a geostatistical ensemble square root filter that isused to estimate CO2 surface fluxes over North America us-ing ground-based continuous measurements for 2008. Thegeostatistical ensemble square root filter is a novel methodthat is being developed to take advantage of both the ver-satility of a geostatistical inverse modeling framework, andof the computational efficiency of the ensemble approach.This presentation will not only focus on the methodologicalframework driving the geostatistical ensemble square rootfilter but also on comparing the results from the filter witha batch solution for the same problem. The sensitivity ofboth estimates and their uncertainties due to a shift fromgeostatistical batch inversion to a geostatistical ensembletechnique will be analyzed. Further discussions will centrearound the properties of the filter (for example, impact ofensemble size, representation of error covariances and theirpropagation, adaptive inflation etc.) and the overall frame-work required to reduce the computational cost associatedwith CO2 source/sink estimation while providing a best es-timate and estimated uncertainty equivalent to traditionalbatch inversions.

Abhishek Chatterjee, Vineet Yadav, Kim Mueller, SharonGourdji, Anna MichalakUniversity of Michiganabhishch@umich.edu, vineety@umich.edu,kimlm@umich.edu, sgourdji@umich.edu,amichala@umich.edu

MS18

Quantification of Uncertainty for the VulcanProject High Resolution Fossil Fuel CO2 EmissionsData Product

Abstract not available at time of publication.

Kevin GurneyArizona State Universitykevin.gurney@asu.edu

MS18

Ensemble Kalman Filters Applied to CO2 SourceInversion

We present a numerical study using a hybrid EnsembleKalman Filtering (EnKF) algorithm to invert for CO2sources. The underlying transport model is a convection-diffusion model in which the source terms are representedby the pixels of a satellite image of the US at night. Theintensity of the lights represents the magnitude of the emis-sions. We investigate the use of this model as prior infor-mation in the EnKF based inversion.

Bart van Bloeman Waanders, Sean McKennaSandia National Laboratoriesbartv@sandia.gov, samckenna@sandia.gov

Jaideep RaySandia National Laboratories, Livermore, CAjairay@sandia.gov

MS19

Mesh-independent Finite Element Methods forEarthquake Simulation

Earthquake simulation is complicated by the complex na-ture of faults which rupture. Faithful representation of thefault network geometry and solution robustness to varia-tion of this geometry have proven difficult problems forstandard finite element methods, which require simulationmeshes to conform to the faults. Here we present a mesh-independent method, in which faults are included indepen-dently of the simulation mesh. We demonstrate the versa-tility of the method in earthquake and crustal deformationsimulations.

Ethan T. CoonLos Alamos National Laboratoryecoon@lanl.gov

Bruce ShawColumbia Universityshaw@ldeo.columbia.edu

Marc SpeigelmanLamont Doherty Earth Observatorymspieg@ldeo.columbia.edu

MS19

Large-scale Earthquake Simulations and the Pre-diction of Strong Ground Motion

Accurate, scalable numerical simulations of earthquakeruptures and the concomitant excitation and propagationof stress waves in realistic three-dimensional geologic mod-els are important to our understanding of the physics ofearthquakes and the prediction of strong ground motion.We give an overview of some insights that have accruedfrom recent large-scale simulations. These have revealedunexpected interactions between the source and the geo-logic structure that have been further illuminated by ad-joint simulations.

Steven DayDept of Geological SciencesSan Diego State universityday@moho.sdsu.edu

Kim OlsenDept of Geological SciencesSan Diego State Universitykbolsen@geology.sdsu.edu

Yifeng CuiSan Diego Supercomputer Centeryfcui@sdsc.edu

MS19

Adaptive Mesh Refinement for Earthquake Rup-ture Simulations

Strong shaking from large earthquakes extends tens to hun-dreds kilometers from faults of comparable size, but nu-merically resolving laboratory-constrained frictional pro-cesses requires millimeter to centimeter grid spacings. Con-strained by current computational resources, the standardmodeling approach is to use approximately constant gridspacings with artificially increased frictional length scales.We present an alternative approach that uses adaptive

GS11 Abstracts 85

mesh refinement to exploit the fact that fine-scale reso-lution needs are localized around the propagating rupturefront.

Jeremy E. KozdonStanford UniversityGeophysicsjkozdon@stanford.edu

Eric M. DunhamDepartment of GeophysicsStanford Universityedunham@stanford.edu

MS19

Simulations of Long-term Slip of Earthquake-producing Faults: Importance of IncorporatingFull Inertial Effects during Seismic Slip

We study mechanics and physics of earthquakes using aunique modeling approach that reproduces both earth-quakes and slow slip, with full inclusion of inertial effectsduring simulated earthquakes. Here, we compare this ap-proach to a popular simplified, so-called quasi-dynamic,method, in which inertial effects are incorporated througha radiation damping approximation. We find that the twomethods can produce qualitatively different earthquakesand long-term fault behavior. Our eventual goal is to de-termine the range of applicability for the quasi-dynamicapproaches.

Nadia Lapusta, Marion Thomas, Hiro Noda,Jean-Philippe AvouacCalifornia Institute of Technologylapusta@caltech.edu, marion@gps.caltech.edu,hnoda@caltech.edu, avouac@gps.caltech.edu

MS20

An Energy-conserving Discontinuous MultiscaleFinite Element Method for the Wave Equation inHeterogeneous Media

In this talk, we present a new multiscale finite elementalgorithm for simulating acoustic wave propagation in het-erogeneous media. This method solves the wave equationon a coarse grid using multiscale basis functions and a cou-pling mechanism to relate information between fine andcoarse grids. Our method is based on a mixed formu-lation of the wave equation and staggered discontinuousbasis functions. Thus, our multiscale methods have thefollowing nice properties. (1) The total wave energy is con-served, (2) Mass matrix is diagonal on a coarse grid andenergy-preserving, and (3) Multiscale basis functions canaccurately capture the subgrid behavior. Some numericalresults will be shown. This is a joint work with YalchinEfendiev and Richard Gibson.

Eric ChungThe Chinese University of Hong KongDepartment of Mathematicstschung@math.cuhk.edu.hk

MS20

A Bayesian Uncertainty Quantification of Frac-tured Reservoirs using Surrogate Flow Model

The modeling of fractured reservoirs typically involves sep-aration of the matrix and fracture parameters, and we be-

gin by introducing a surrogate dual porosity, dual perme-ability model for tracer flow in this type of system. Toquantify the uncertainty, the ideal situation is to inte-grate available static and dynamic data into this surrogatemodel. This is accomplished within a Bayesian frameworkusing Markov Chain Monte Carlo methodology. A num-ber of numerical examples are presented to illustrate theperformance of the method.

Victor E. GintingDepartment of MathematicsUniversity of Wyomingvginting@uwyo.edu

MS20

A New Problem Adapted Hierarchical Model Re-duction Technique Based on Reduced Basis Meth-ods and Dimensional Splitting

We present a new dimension reduction technique [M.Ohlberger and K. Smetana, 2010]. In comparison to theBoussinesq approach we do not neglect the dependency onthe vertical direction but enhance the solution for the hor-izontal direction with appropriately chosen basis functionsliving on the vertical one. This is done by a combinationof the frameworks of hierarchical model reduction [S. Per-otto, A. Ern, and A. Veneziani, 2010] and the reduced basismethods [B. Haasdonk, M. Dihlmann and M. Ohlberger,2010]. We derive a new a posteriori error estimate anddemonstrate in numerical experiments that few basis func-tions suffice to get good approximations.

Kathrin SmetanaInstitute for Computational and Applied Mathematics,Westfaelische Wilhelms-University Muensterkathrin.smetana@uni-muenster.de

Mario OhlbergerUniversitat MunsterInstitut fur Numerische und Angewandte Mathematikmario.ohlberger@uni-muenster.de

MS21

A Practical Modeling Approach to Evaluate Long-term CO2 Storage in Real Geological Systems

Large-scale models of CO2 injection into geological forma-tions must capture the relevant geological and geophysicalprocesses that affect the migration and ultimate fate of in-jected CO2. These processes span many spatial and tempo-ral scales, and traditional numerical methods cannot solvethese large, complex systems in a practical way. A newmodeling approach solves coarse-scale vertically-integratedgoverning equations that are coupled with subgrid modelsto capture important small-scale processes in an efficientand accurate way.

Sarah GasdaUniversity of North Carolina at Chapel Hillsgasda@unc.edu

Jan M. NordbottenDepartment of MathematicsUniversity of Bergenjan.nordbotten@math.uib.no

Michael A. CeliaPrinceton UniversityDept of Civil Engineering

86 GS11 Abstracts

celia@princeton.edu

MS21

The Effect of Capillary Forces on Two-phase Flow

We derive a two-phase gravity current model from frac-tional flow theory under the assumption large aspect ratioand vertical gravity-capillary equilibrium. The saturationprofile in combination with the relative permeability deter-mines the dynamics of the two-phase current. The modelsignificantly improves estimates of the vertical sweep, themagnitude of residual trapping, and the propagation speedof the current. This model provides physical insight andan efficient formulation for large scale geological carbondioxide storage.

Marc A. HesseUniversity of TexasDepartment of Geological Sciencesmhesse@jsg.utexas.edu

Madeleine GoldingCambridge Universitymjg88@cam.ac.uk

Jerome NeufeldCambridge UniversityDepartment of Applied Mathematics and TheoreticalPhysicsjn271@cam.ac.uk

MS21

Stochastic Inversion of Seismic and Electromag-netic Data for Co2 Saturation Prediction

Stochastic inversion of seismic (AVA) and electromagnetic(CSEM) data are used to predict CO2 saturation. A 2Dsynthetic model constructed for hydrocarbon explorationhas been adapted to fill the reservoirs with CO2. Syntheticseismic and CSEM data are used to test the resolution ofCO2 saturation predictions under a range of experimentalvariables. The choice of rock physics model, the proximityof wells used for rock physics, noise levels and choice ofgeophysical forward models all effect the quality of the CO2saturation prediction.

G. Michael HoverstenChevron Energy Technology Companyhovg@chevron.com

Jinsong ChenLawrence Berkeley National Laboratoryjchen@lbl.gov

MS21

Time-lapse Wave-equation Imaging of CO2 Geose-questration

Time-lapse seismic monitoring of CO2 geosequestrationis emerging as an important geophysical research field.Most 4D seismic inversions for estimating elastic propertychange are linearized about baseline elastic models. Large-scale CO2 injection, though, can introduce large propertyperturbations that lead to complex wavefield coda and astrongly non-linear inversion problem. We demonstratethat overcoming this non-linearity requires a time-lapseseismic inversion procedure that includes 4D depth velocity

analysis and migration.

Jeffrey C. Shragge, David LumleyUniversity of Western Australiajeffrey.shragge@uwa.edu.au, david.lumley@uwa.edu.au

MS21

The Rock Physico-chemical Basis for Time-lapseSeismic Reservoir Monitoring of CO2 Injection

4D laboratory experiments, high-resolution imaging, andcomputational rock physics are used to monitor the effectof physicochemical processes occurring upon injection ofCO2 within sandstone and carbonate rocks. The goal is tounderstand the effect of salt precipitation and dissolutionon transport and seismic properties and verify the need forextending tools currently available in rock physics to in-fer subsurface conditions where the coupling between porefluids and rock matrices is not purely mechanical. Resultsshow that the seismic response of CO2-brine-rock systemsis far from being a pure fluid-substitution problem.

Tiziana VanorioDepartment of GeophysicsStanford Universitytvanorio@stanford.edu

Elizabeth DiazIngrain Inc.diaz@ingrainrocks.com

Amos NurStanford UniversityIngrain Inc.anur@stanford.edu

MS22

Mixed Hybrid and Linear Conforming Finite Ele-ments for the Simulation of Reactive Multicompo-nent Transport in Porous Media

Mixed hybrid FE are applied to reactive transport inporous media and compared to linear conforming FE withrespect to the numerical diffusion they introduce and theirbehavior in the case of discontinuous coefficient functions.A general discretization of the nonlinear transport-reactionequations with RT0, BDM1 and RT1 elements is shown.We present numerical tests giving evidence that mixedschemes may be preferable for this application where theprimary unknown is not a vector variable.

Fabian BrunnerUniversity of Erlangenbrunner@am.uni-erlangen.de

MS22

A More Robust MHFE Scheme for Solute Trans-port in Porous Media

We present a new, more robust mass conservative finiteelement scheme for reactive solute transport in porousmedia. The transport is modelled by a convection-diffusion-reaction equation, including equilibrium or non-equilibrium sorption. The numerical scheme is based onmixed hybrid finite elements (MHFE) and it is more effi-cient for high Peclet numbers as the classical one [1]. Thelowest order Raviart-Thomas elements are used. We alsopresent an upwind variant of it, which should be consid-

GS11 Abstracts 87

ered for strong convection dominated problems. Variousnumerical tests, including the case of heterogeneous soilare shown.

REFERENCES

F.A. Radu, N. Suciu, J. Hoffmann, A. Vogel, O. Kolditz,C-H. Park and S. Attinger. Accuracy of numerical simula-tions of contaminant transport in heterogeneous aquifers:a comparative study. Advances in Water Resources, 2010,doi:10.1016/j.advwatres.2010.09.012.

Florin A. RaduUFZ-Helmholtz Center for Environmental Research,LeipzigGermanyflorin.radu@ufz.de

MS22

Convergence and Interpolation of Numerical RawField Methods on General Grids

We discuss conditions and limitations for convergence ofsome multi-point flux approximation (MPFA) methods onpolyhedral meshes in the presence of a discontinuous per-meability field. In a more general setting we look at whatthe difference between raw field methods (like the MPFAand mimetic FD methods) and full field methods (like themixed finite element method) implies and the importanceof interpolation. Our discussion is supplemented with someillustrative numerical examples

Runhild A. KlausenUniversity of OsloNorwayrunhildk@cma.uio.no

Annette Stephansen

CIPR / University of Bergenannette.stephansen@uni.no

MS22

Guaranteed and Robust a Posteriori Stopping Cri-teria for Iterative Linearizations and Linear Solvers

We present a posteriori error estimates of the linearizationerror in approximation of nonlinear problems and of thealgebraic error in the solution of linear systems and derivestopping criteria for (non)linear iterations. Our estimatescontrol the overall error. They are also locally efficientand thus allow to predict the error spatial distribution andto refine the mesh adaptively. We present strategies forachieving a user-specified accuracy at minimal cost andillustrative numerical experiments.

Linda El AlaouiLAGA, Universite Paris 13Villetaneuse, Franceelalaoui@math.univ-paris13.fr

Alexandre ErnUniversite Paris-EstCERMICS, Ecole des Pontsern@cermics.enpc.fr

Pavel JiranekCERFACSToulouse, Francepavel.jiranek@cerfacs.fr

Zdenek StrakosDepartment of numerical mathematics, Charles UniversityPrague, Czech Republicstrakos@karlin.mff.cuni.cz

Martin VohralikUniversite Pierre et Marie CurieParis, Francevohralik@ann.jussieu.fr

MS23

Continuous and Discontinuous Data AssimilationMethods for Estimating a Heterogeneous Conduc-tivity Field by Assimilating Transient Solute Trans-port Data

An ensemble Kalman Filter (EnKF) is developed to iden-tify a hydraulic conductivity distribution in a heteroge-neous medium by assimilating solute concentration mea-surements of solute transport in the field with a steadystate flow. A synthetic case with the mixed Neumann/Dirichlet boundary conditions is designed to investigate thecapacity and effectiveness of the proposed continuous anddiscontinuous data assimilation methods to identify a con-ductivity distribution. The developed method is demon-strated in 2-D transient solute transport. The study resultsindicate that the EnKF method will significantly improvethe estimation of the hydraulic conductivity field by as-similating continuous or discontinuous solute concentrationmeasurements. In comparison with the continuous dataassimilation method, the discontinuous data assimilationmethod can better identify the heterogeneous conductivityfield, especially in the downstream flow field

Bill HuEarth, Ocean and Atmospheric SciencesFlorida State Universitybill.x.hu@gmail.com

MS23

Some Recent Advances in the Scaling of Earth andEnvironmental Variables

It has been demonstrated theoretically and numericallyby the author that data sampled from fractional Gaus-sian/Levy noise (fGn/fLn) exhibit apparent/spurious mul-tifractality. Here we generalize Neuman’s development ina way that (a) rigorously subordinates (truncated) fLn to(truncated) fGn, (b) extends the analysis to a wider classof subordinated self-affine processes and (c) explains whythe distribution of corresponding data tends to evolve fromheavy tailed at small lags (separation distances or scales)to Gaussian at larger lags.

Shlomo NeumanUniversity of ArizonaDepartment of Hydrology and Water Resourcesspneuman@comcast.net

MS23

Uncertainty Quantification in Subsurface Modeling

We consider a a set of parabolic partial differential equa-tions with uncertain coefficients that describe flow andtransport in heterogeneous porous media. To quantifypredictive uncertainty in such systems, we treat uncertaincoefficients as random fields with known statistics, whichrenders the corresponding governing nonlinear differential

88 GS11 Abstracts

equations stochastic. We derive a deterministic equationfor the probability density function (PDF) of the systemstate. By going beyond computing system state’s meanand variance, which is the standard practice in many un-certainty quantification studies, the PDF equations enableone to compute probabilities of rare events (distributiontails), which are required in modern probabilistic risk anal-yses.

Daniel M. TartakovskyUniversity of California, San Diegodmt@ucsd.edu

Marco DentzIDAEASpanish National Research Council (CSIC)marco.dentz@idaea.csic.es

MS23

Iterative Coupling for Treating CompositionalFlow and Geomechanics

We formulate a scheme for coupling an equation of state(EOS) compositional flow model with elasticity. We dis-cuss iterative coupling, discretizations, solvers, and parallelscaling issues.

Mary F. WheelerCenter for Subsurface ModelingUniversity of Texas at Austinmfw@ices.utexas.edu

MS24

Interface Conditions for Fluid Flow in Porous Me-dia withReduced Order and Non Matching Frac-tures

For large scale computations of flows in porous media withcomplex fracture networks the conformity of the mesh canrepresent a severe constraint. We propose a method thatallows for non-matching grids, thus very advantageous ifthe position of the fractures is uncertain and multiple sim-ulations are required. We consider mixed hybridized finiteelements for the discretization of the bulk flow and thereduced problem in the fractures and provide the correctinterface conditions.

Alessio FumagalliMOX, Politecnico di MilanoItalyalessio.fumagalli@polimi.it

Anna ScottiPolitecnico di Milanoanna.scotti@mail.polimi.it

Carlo D’AngeloMOX - Department of MathematicsPolitecnico di Milanocarlo.dangelo@polimi.it

MS24

Darcy-Stokes Fracture Flow

The asymptotic analysis of Darcy flow in a region coupledto Stokes flow in a very thin fracture is revisited. The ap-propriately scaled model leads to a limiting problem con-sisting of Darcy flow in the region coupled to Brinkmann

flow in the fracture.

Fernando Morales, Ralph ShowalterDepartment of MathematicsOregon State Universitymoralefe@math.oregonstate.edu,show@math.oregonstate.edu

MS24

Schur Complement Preconditioning for Flow Sim-ulation in 3D Discrete Fracture Networks

The simulation of flow in discrete fractured media requiresto solve very large linear systems. Those systems are sparseand with a specific shape due to the underlying physicalproblem. In order to take advantage of this specific struc-ture, a preconditioned conjugate gradient method basedon the Schur complement is used. Several preconditioningapproaches are tested. We present simulations results insequential as well as in parallel.

Baptiste PoirriezINRIA RennesUniversity of Rennes 1baptiste.poirriez@irisa.fr

Jocelyn Erhel, Geraldine PichotINRIA Rennes Bretagne AtlantiqueFrancejocelyne.erhel@inria.fr, geraldine.pichot@inria.fr

MS24

Modeling Fluid Flow Along Faults

We study an approach to model fluid flow along faultcompatible with the standard oil industry flow simulatorswhere faults are represented by interfaces across which thegrid does not match. The fault zone is represented by twosets of faces, each set matching its neighbouring matrixcells, and flow is modeled by a surface model. We presentresults ranging from academic cases to one phase flow inbasin modeling where sliding along faults occurs.

Isabelle Faille, Marie-Christine CacasIFP Energies NouvellesFranceisabelle.faille@ifpenergiesnouvelles.fr,m-christine.cacas@ifpenergiesnouvelles.fr

Thierry GallouetUniversite de Provencegallouet@cmi.univ-mrs.fr

Pascal Have, Roland Masson, Xavier Tunc, FrancoiseWillienIFP Energies NouvellesFrancepascal.have@ifpenergiesnouvelles.fr,roland.masson@ifpenergiesnouvelles.fr,xavier.tunc@ifpenergiesnouvelles.fr,francoise.willien@ifpenergiesnouvelles.fr

MS25

On Stability of the Fluid Structure Interaction inPorous Media fo Non-linear Potential Flows

In this work we consider the dynamical response of a non-linear plate with viscous damping interacting with a non-

GS11 Abstracts 89

linear potential flow. The system is modeled using non-linear momentum equations for the axial and transversedisplacements coupled with fluid flow subjected to Forch-heimer type flow. In particular we show that for a classof boundary conditions given inlet velocity flow for liquid,dynamic of the process is stable with respect to boundaryinput Data.

Eugenio AulisaDepartment of Mathematics and Statistics.Texas Tech Universityeugenio.aulisa@ttu.edu

Luan HoangTexas Tech UniversityDepartment of Mathematics and Statisticsluan.hoang@ttu.edu

Yasemen KayaDepartment of MathematicsTexas Tech Universityyasemen.kaya@ttu.edu

MS25

Multi-scale Modeling of Brinkman’s Filtration inLayered Porous Media

We applied the theory of homogenization to the case ofBrinkman filtration of viscous incompressible fluid throughheterogeneous porous medium, whose material structurewas characterized by periodicity over several length scales.We derived governing equations for all scales and obtainedgeneral relationships between the pressure and the velocityof fluid. The derivation of effective coefficients was reducedto the solution of periodic problems in cells, which weresolved numerically.

Viktoria SavatorovaPhysics Department,National Research Nuclear Universitysvl97@rambler.ru

MS25

On a Power Series Solution to the Boussinesq Equa-tion

The Boussinesq equation describes water flows in uncon-fined groundwater aquifers under the Dupuit assumptionthat the equipotential lines are vertical, making flow hori-zontal. It is a nonlinear diffusion equation with diffusivitydepending linearly on water head. We also analyze a gener-alized Boussinesq equation, where the diffusivity is a powerlaw function of water head. For certain classes of initial andboundary conditions approximate analytical solutions canbe constructed using the scaling properties of the equation.

Aleksey S. TelyakovskiyDepartment of Mathematics and StatisticsUniversity of Nevadaalekseyt@unr.edu

MS25

Pore-scale Fluid Dynamical Perspective of Non-Darcy Effects in the Inertial Flows Through Re-alistic Porous Media: A First Principle Analysis of

Forchheimer Relationship

Detailed simulations of single-phase flow in the imaged-based realistic porous media are carried out using LatticeBoltzmann Method (LBM) over a wide range of Reynoldsnumber. Inertial effects manifest themselves as the devia-tion from Darcys law on the macroscopic scales. Transitionfrom viscous forces dominated flow regime to inertia dom-inated flow can be systematically predicted as well as theparameters such as permeability and Forchheimer coeffi-cient can be calculated from three-dimensional flow simu-lations.

Mayank TyagiLSUmtyagi@lsu.edu

MS26

Grid Resolution Requirements and ComputationalOverhead in Nonhydrostatic Coastal Ocean Mod-eling

Computation of the nonhydrostatic pressure may be re-quired in coastal ocean models if the relevant horizontalscales of motion are on the same order as the vertical scales.I will present a method to determine how much grid reso-lution is required to resolve nonhydrostatic processes. Al-though solution of the nonhydrostatic pressure can be ex-pensive, I will show that weakly nonhydrostatic processescan incur minimal overhead with the use of appropriatepreconditioners.

Oliver FringerEnvironmental Fluid Mechanics LaboratoryStanford Universityfringer@stanford.edu

MS26

Modeling Storm Surges with the Multilayer Shal-low Water Equations

Storm surges created by tropical storms pose significantflooding risks to coastal populations. Many current modelsof surge use the single layer shallow water equations, whichcapture much of the physics while allowing rapid compu-tation over vast regions. We are examining the potentialadvantages of using the multilayer shallow water equationstogether with adaptive mesh refinement to efficiently cap-ture additional storm surge physics.

Kyle T. MandliUniversity of WashingtonDept. of Applied Mathematicsmandli@amath.washington.edu

Randall J. LeVequeApplied MathematicsUniversity of Washington (Seattle)rjl@uw.edu; rjl@amath.washington.edu; rjl@washingt

MS26

Title Not Available at Time of Publication

Abstract not available at time of publication.

Joannes WesterinkDepartment of Civil Engineering and Geological SciencesUniversity of Notre Damejoannes.j.westerink.1@nd.edu

90 GS11 Abstracts

MS26

Challenges in 3D Cross-Scale Modeling

Originally developed as a 3D baroclinic circulationmodel for the Columbia River estuary-plume-shelf sys-tem, SELFE (Semi-implicit Eulerian-Lagrangian Finite El-ement) has evolved into a comprehensive, open-sourcecommunity-supported modeling system. Grounded on un-structured grids, the model is designed for the effectivesimulation of 3D baroclinic/barotropic flows across river-to-ocean scales. It uses an efficient semi-implicit finite-element Eulerian-Lagrangian method to solve the Navier-Stokes equations (in either hydrostatic or non-hydrostaticform), written in MPI FORTRAN90 to realistically ad-dress a wide range of physical processes and of atmospheric,ocean and river forcings. The combination of unstructuredgrids, implicit time stepping and an Eulerian-LagrangianMethod in SELFE leads to superior flexibility, accuracy,efficiency and robustness. We present new developmentsof the SELFE modeling system in the areas of 3D baro-clinic circulations, tsunami and storm surge inundation (in-cluding wave-current interaction). The cross-scale natureof the SELFE modeling system (from minutes to decade,and from meters to hundreds of kilometers) also presentsgreat computational/algorithmic challenges (e.g. wettingand drying; multi-physics in a single modeling frameworketc) that beckon applied mathematicians to address.

Yinglong J. ZhangCMOP, OHSUyinglong@stccmop.org

MS27

Overview of Upscaling, Multiscale and Reduced-order Modeling Techniques for Subsurface Flow

A wide variety of upscaling (numerical homogenization),multiscale modeling, and reduced-order modeling proce-dures have been developed for subsurface flow simulation.We will briefly discuss these general approaches, highlight-ing key similarities and differences. Then, a trajectorypiecewise linearization approach will be described. Thistechnique, which entails linearization around saved statesand a POD-based projection into a low-dimensional sub-space, is applied for subsurface flow modeling. Some exist-ing challenges will also be discussed.

Lou DurlofskyEnergy Resources Engineering DepartmentStanford Universitylou@stanford.edu

MS27

Parameterized Model-Order Reduction for Large-Scale Reservoir Models

In this presentation, we investigate the use of the para-metric model order reduction(PMOR) techniques appliedto porous media flow simulation in a system-theoreticalframework. PMOR entails the generation of reduced-ordermodels which retains the functional dependency on spe-cific parameters of the original large-scale system. Usually,an ensemble of models is used to assess uncertainty in thereservoir simulation. In order to overcome the computa-tional effort in this scenario, reduced-order models thattake into account this entire ensemble are necessary to ob-tain.

Eduardo Gildin

Center for Subsurface ModelingUniversity of Texas at Austinegildin@mail.utexas.edu

MS27

Pressure Preconditioning Using Proper Orthogo-nal Decomposition

We developed and implemented a new physics-based pre-conditioning method for solving the pressure equation inlarge-scale reservoir simulation as an alternative to thepopular Algebraic Multi Grid (AMG) method. The newmethod uses a small set of pre-computed pressure solutionsto transform the pressure equation into a lower-order rep-resentation using Proper Orthogonal Decomposition. Intest cases we reduced the linear solver time by about 50%compared to AMG preconditioning.

Jan Dirk JansenTechnische Universiteit DelftShell International E&Pj.d.jansen@tudelft.nl

MS27

A local POD-Based Multicale Mixed FEM forModel Reduction of Multiphase Compressible Flow

We develop a local basis model-order reduction techniquefor approximation of flux/pressure fields based on lo-cal proper orthogonal decompositions (PODs) consistentlyglued together using the Multiscale Mixed FEM (MsM-FEM) framework on a coarse grid. Based on snapshotsfrom one or more simulation run, we perform SVDs for theflux distribution over coarse grid interfaces and use the sin-gular vectors corresponding the largest singular values asboundary conditions for the multiscale flux basis functions.The span of these basis functions matches (to prescribedaccuracy) the span of the snapshots over coarse grid faces.Accordingly, the complementary span (whats left) can beapproximated by local PODs on each coarse block givinga second set of local/sparse basis functions. The reducedsystem unknowns corresponding to the second set of basisfunctions can be eliminated to keep the system size low.To assess the accuracy, we apply the methodology to a re-alistic test problem (two-phase compressible flow includinggravity) with several wells and compare to results obtainedfrom full order simulations. Both changing well configura-tions and changing well placements (with local update ofbases) are considered. In addition, comparison to standardPOD is considered.

Stein KrogstadSINTEF ICTStein.Krogstad@sintef.no

MS28

CO2 Geological Storage and Groundwater Re-sources: Model Applications

This paper provides an overview of research issues andmodeling applications related to understanding potentialimpacts of geologic carbon sequestration on groundwaterresources. Issues addressed by multi-phase modeling andreactive transport simulations include (1) the possibility ofwater quality changes due to leakage of CO2 (together withco-migrating contaminants) into fresh water aquifers, and(2) the potential of regional-scale hydrogeologic perturba-tion caused by the injection of CO2 and the subsequent

GS11 Abstracts 91

displacement of native brine.

Jens T. BirkholzerLawrence Berkeley National Laboratory(LBNL)JTBirkholzer@lbl.gov

Quanlin Zhou, Liange Zheng, Nicolas SpycherLawrence Berkeley National Laboratory (LBNL)qzhou@lbl.gov, lzheng@lbl.gov, nspycher@lbl.gov

MS28

Variations of CO2/Water Interfacial Tension andImpact on CO2 Trapping Capacity

We have implemented an empirical correlation for wa-ter/CO2 interfacial tension (IFT) in the compositional flowand reactive module of IPARS parallel reservoir simulator.The IFT correlation is a function of pressure, salinity, andtemperature. The relative permeabilities are generalized toaccount for combined effects of viscous, buoyancy, and cap-illary forces. Several prototype aquifer models are studiedto determine the impact of injection rates and IFT varia-tions on CO2 migration and trapping.

Mojdeh DelshadDepartment of Petroleum and Geosystems EngineeringThe University of Texas at Austindelshad@mail.utexas.edu

Xianhui KongCenter for Subsurface ModelingThe University of Texas at Austinxhkong@mail.utexas.edu

Mary F. WheelerCenter for Subsurface ModelingUniversity of Texas at Austinmfw@ices.utexas.edu

MS28

Title Not Available at Time of Publication

Abstract not available at timr of publication.

Margot GerritsenDept of Petroleum EngineeringStanford Universitymargot.gerritsen@stanford.edu

MS28

Analysis of Capillary Structures in HeterogeneousFormations

Local capillary trapping is a potentially important mech-anism for immobilization of CO2. It occurs at smallscales (compared to field scale) as CO2 rises under gravitythrough heterogeneous formations. The overall objectiveis to analyze the structures that could form local capillarytraps in typical storage formations. We generate geosta-tistical realizations of permeability from variogram modelspopulated with key petrophysical properties and analyzespatial properties of them to determine the potential forlocal capillary trapping.

Ehsan SaadatpoorDepartment of Petroleum and Geosystems EngineeringThe University of Texas at Austin

ehsan@mail.utexas.edu

Steven L. BryantPetroleum and Geosystems Engineering DepartmentUniversity of Texas at Austinsteven bryant@mail.utexas.edu

Kamy SepehrnooriDepartment of Petroleum and Geosystems Engineeringkamys@mail.utexas.edu

MS28

Multiscale Numerical and Physical Modeling ofGeologic Carbon Sequestration

Geologic carbon sequestration is impacted by several pro-cesses including multiphase flow with density and thermaleffects, dissolution of fluid phases, and reactions with reser-voir solids. These are largely controlled by pore-scale (mi-cron to mm-scale) features of the fluid interfaces and solidmaterial surfaces, while quantitative predictions are neededat much larger length scales. We will present a suite of nu-merical and physical models defined at the pore scale andtheir application to field-scale simulations.

Timothy D. ScheibeHydrology Technical GroupPacific Northwest National Laboratorytim.scheibe@pnl.gov

Alexandre Tartakovsky, Mart Oostrom, Mark D. WhitePacific Northwest National Laboratoryalexandre.tartakovsky@pnl.gov, mart.oostrom@pnl.gov,mark.white@pnl.gov

MS29

Finite Volume Approximation for Two-phase Flowswith Discontinuous Capillary Pressure

We are interested in a PDE system describing an incom-pressible immiscible two-phase flow in a porous mediummade of two different rocks. Since the capillary pressurefunction depends on the rock type, the capillary pressurefield can be discontinuous at the interface between therocks. We give a sense to the transmission conditions atthe interface, and then, we propose a Finite Volume schemeallowing to deal with such discontinuities, and prove itsconvergence towards a weak solution to the problem.

Konstantin BrennerUniversite Paris Sud (Orsay)konstantin.brenner@math.u-psud.fr

Clement CancesUniversite Pierre et Marie Curie , Paris, Francecances@ann.jussieu.fr

Danielle HilhorstUniversite Paris Sud (Orsay)danielle hilhorst ¡danielle.hilhorst@math.u-psud.f

MS29

A New Corrected Operator Splitting Method Com-bining Streamline Approach for Two-phase Flowwith Gravity

Gravity is important for dynamics which often cannot be

92 GS11 Abstracts

neglected but poses significant challenges for the numeri-cal approximation of PDEs. Thus, this talk focuses on anew corrected operator splitting (COS) method for higher-dimensional two-phase flow problems with gravity, and theCOS method is devised by handling the gravity term basedon streamline tracing for a front velocity field generatedfrom flux splitting. Different numerical examples are sim-ulated and explained.

Yufei CaoIWS, University of Stuttgart, Germanyyufei.cao.prc@googlemail.com

Magne S. EspedalDepartment of Mathematics,University of Bergen, Norwaymagne.espedal@math.uib.no

Rainer HelmigIWS, University of Stuttgart, GermanyInstitut fur Wasserbaurainer.helmig@iws.uni-stuttgart.de

Barbara WohlmuthM2, Centre for Mathematical Sciences,Technische Universitat Munchen, Germanybarbara.wohlmuth@ma.tum.de

MS29

The Application of Homogenization Theory toStudy the Stability of Density-driven Flows in Het-erogeneous Formations

Density-driven flows cut across many practical applicationslike normal and nuclear waste repository management, theprotection of coastal groundwater aquifers from salty sea-water intrusion, the harnessing of geothermal resources andthe exploration of petroleum. A typical feature of such sys-tems is that they can become unstable and exhibit the fin-gering phenomenon. A salient challenge to-date has beenthe absence of a stability criterion capable of predicting theonset of fingering. In this work we apply homogenizationtheory techniques developed in [Held et al. 2005] to derivethe small- and large-scale transport equations [Musuuzaet al., (2009)]. The small-scale equation is used to derivea stability criterion in terms of the density, dispersivities[Musuuza et al., (2010)] and heterogeneity properties. Thecriterion is tested on those variables and produced reason-able predictions for the onset of convection. The large-scaleequation is used to study mixing behaviour by evaluatingthe macrodispersion tensor elements. The system stabil-ity could be inferred from the temporal evolution of thelongitudinal coefficient.

Jude L. MusuuzaUniversity of Jenajude.musuuza@uni-jena.de

Florin A. RaduUFZ-Helmholtz Center for Environmental Research,LeipzigGermanyflorin.radu@ufz.de

Sabine AttingerInstitute of Computational ComputationalEnvironmentaScienceUFZ Leipzigsabine.attinger@ufz.de

MS29

Convergence Analysis of a Vertex-centered FiniteVolume Scheme for a Copper Heap Leaching Model

This work is motivated by a combined mixed finite element(MFE) - finite volume (FV) scheme of a two phase flowmodel for the heap leaching of copper ores modeled by adegenerate parabolic equation

∂tu −∇ · (∇β(u) + F (u)) = r(u), in QT ≡ (0, T ) × Ω.

Initially we have u(0) = u0 in Ω, whereas u = 0 on ∂Ω.In the above 0 < T < ∞ is fixed, Ω is a bounded do-main in Rd(d ≥ 1) with a Lipschitz continuous bound-ary. The function β : R → R is non-decreasing anddifferentiable. By degeneracy we mean a vanishing dif-fusion, namely β′(u) = 0 for some u. We prove error es-timates for the finite volume discretization for this model.Then, a two-dimensional solute transport model is con-sidered to simulate the leaching of copper ore tailing us-ing sulfuric acid as the leaching agent. The mathemat-ical model consists in a system of differential equations:two diffusion-convection-reaction equations with Neumannboundary conditions, and one ordinary differential equa-tion. The numerical scheme consists in a combination offinite volume and finite element methods. Some numericalexamples illustrate the effectiveness of the scheme.

Mauricio SepulvedaUniversidad de Concepcionmauricio@ing-mat.udec.cl

MS30

Porous Media Research at Purdue: Past and Fu-ture

My group has focused on four basic porous media prob-lems over the years, i) swelling porous media (mixture the-ory and homogenization), ii) nano films (computationalchemistry), iii) diffusion/dispersion in heterogeneous me-dia (stochastic perturbation, CLTs, and statistical mechan-ics) and iv)nutrient transport to growing roots (non-linearmoving BCs for diffusion problems). Each of these topicswill be briefly discussed in the context of my students andpost docs efforts. A brief look toward the future will bepresented.

John H. CushmanDepartment of MathematicsPurdue Universityjcushman@purdue.edu

MS30

Polar Field Theories: Small Scale to Large ScaleApplications

Micromorphic fluids contain a particulate substructurewhich affects the movement of the fluid. This structurecan be incorporated into the fluid flow model. This talkwill present two models using these fluids including smalland large scale examples. Current work initiated by Dr.Cushman and associates related to large scale continentaldeformation will be discussed. The continental plates arebeing viewed as micropolar bodies with substructures thatcan rotate in addition to the translational movement.

Natalie Kleinfelter DomelleMathematics DepartmentSaint Marys Collegendomelle@saintmarys.edu

GS11 Abstracts 93

John H. CushmanDepartment of MathematicsPurdue Universityjcushman@purdue.edu

MS30

Modeling Coupled Hydrological and Chemical Pro-cesses in Unsaturated Fractured Porous Media

Environmental remediation often leads to geochemicaltransformations, such as precipitation and dissolution ofminerals and evolution of gases and bio-films. These trans-formations may in turn modify the hydraulic properties ofthe system. If significant changes take place in either theflow paths or the hydraulic properties, they may have animpact on the geochemical transport processes. We showhow transient changes in hydrological properties caused bycoupling of hydrological and chemical processes often leadto local flow channeling and saturation increases in unsat-urated fractured porous media.

Sumit Mukhopadhyay

Earth Sciences Division/HydrogeologyLawrence Berkeley National Laboratorysmukhopadhyay@lbl.gov

MS30

Computation of Flow and Transport in Large andSparse Fracture Networks

The discrete fracture network (DFN) approach to computeflow in large two-dimensional fracture networks is an accu-rate but computationally intensive methodology. Contin-uum based methods allow for simulation of processes notpresently achievable using DFN approach but can sufferfrom lack of accuracy especially in prediction of transportbehavior and in cases with sparse fracture networks. Tech-niques to improve the computational efficiency of DFNmethod and predictive accuracy of a continuum methodare presented.

Rishi ParasharDivision of Hydrologic SciencesDesert Research Institute, Reno, NVrishi.parashar@dri.edu

MS31

Two-phase Flow in Porous Media with DiscreteFractures

In this talk we present a discrete fracture model for flow ofa two-phase fluid in a porous medium. Fractures are rep-resented as interfaces and fluid exchange between the frac-tures and surrounding medium is permitted. Thus there isa coupling of n-dimensional flow with (n − 1)-dimensionalflow. The global pressure formulation is used and the frac-ture domain is assumed to be of a rock type different fromthat of the surrounding medium; i.e. the relative perme-ability and capillary pressure curves for the fracture do-main are different from those for the surrounding rock ma-trix. Thus continuity of the saturation can not be assumedin the derivation of the model. The model is implementedwith a mixed finite element method being used in boththe matrix and the fracture but with non matching grids.Numerical results will be shown.

Jerome JaffreINRIA Paris-Rocquencourt

Francejerome.jaffre@inria.fr

Mokhles MnejjaEcole Polytechnique de TunisieTunisiamokhles.mnejja@ept.rnu.tn

Jean E. RobertsINRIA Paris-RocquencourtFrancejean.roberts@inria.fr

MS31

Homogenization Approach to the Quasistatic Cou-pling Poroelastic/ Elastic Media

In this contribution, investigations are focused on the cou-pling of the single phase subsurface flow with poroelastic-ity. Most of the multiscale approaches to Biot’s equationconcentrate on the dynamic case, where memory effectsappear. Here we are interested in the quasistatic case andobtain rigorously the Biot consolidation theory equations.Furthermore, we find the interface conditions between twodifferent flow regimes.

Andro MikelicInstitut Camille Jordan, Departement de MathematiquesUniversite Lyon 1Andro.Mikelic@univ-lyon1.fr

Mary F. WheelerCenter for Subsurface ModelingUniversity of Texas at Austinmfw@ices.utexas.edu

MS31

An Efficient MPFA Approach to Discrete FractureMatrix (DFM) Flow Models

A control volume discretization along with a Multi-Point-Flux Approximation (MPFA) is considered for a DiscreteFracture Matrix (DFM) flow model. Inspired by a recentlyintroduced approach based on Two-Point-Flux Approxima-tion (TPFA), elements in the intersection of fractures areeliminated by a star-delta transformation; hence, avoidingassociated time-step restriction and numerical instabilities.Numerical results demonstrate the flexibility and robust-ness of the new approach.

Tor Harald SandveUniversity of BergenNorwaytor.sandve@math.uib.no

Inga BerreUniversity of BergenChristian Michelsen Researchinga.berre@math.uib.no

Jan Martin NordbottenUniversity of BergenPrinceton Universityjan.nordbotten@math.uib.no

MS31

An XFEM Approach for the Simulation of Frac-

94 GS11 Abstracts

tured Porous-Media Systems

Fractured porous-media systems are simulated, where thecharacteristic flow behaviour depends on the fractures andthe matrix. The global solution is obtained by splittingthe system into a structured rock-matrix grid and an ar-bitrarily orientated fracture network of codimension one.No matching conditions for the two grids are required. Aconsistent weak coupling scheme is developed that is basedon an XFEM approach.

Nicolas SchwenckUniversity of StuttgartNicolas.Schwenck@iws.uni-stuttgart.de

Bernd FlemischUniversity of Stuttgart, Germanybernd.flemisch@iws.uni-stuttgart.de

Barbara WohlmuthUniversity of Stuttgartwohlmuth@ians.uni-stuttgart.de

Rainer HelmigIWS, University of Stuttgart, GermanyInstitut fur Wasserbaurainer.helmig@iws.uni-stuttgart.de

MS32

Performance of the Integrally-Coupled,Unstructured-Mesh SWAN+ADCIRC(DG) Model

The coupling of wave and circulation models is neces-sary to generate waves and surge in deep water, propa-gate them onto the continental shelf, and dissipate themin complex nearshore systems. In this work, the authorscouple the SWAN and ADCIRC(DG) models and investi-gate their performance during a hindcast of Hurricane Ike(2005). The computed circulation is compared betweenADCIRC(CG) and ADCIRC(DG), and its differing effectson the computed wave solution are examined.

Joel C. DietrichDepartment of Civil Engineering and Geological SciencesUniversity of Notre Damedietrich@ices.utexas.edu

Clint Dawson, Jessica MeixnerInstitute for Computational Engineering and SciencesUniversity of Texas at Austinclint@ices.utexas.edu, jmeixner@ices.utexas.edu

Joannes Westerink, Andrew KennedyDepartment of Civil Engineering and Geological SciencesUniversity of Notre Damejjw@nd.edu, andrew.kennedy@nd.edu

Rick LuettichUniversity of North Carolina - Moorehead Cityrick luettich@unc.edu

Marcel Zijlema, Leo HolthuijsenDepartment of Civil Engineering and GeosciencesDelft University of Technologym.zijlema@tudelft.nl, l.h.holthuijsen@tudelt.nl

MS32

Response of Puget Sound to Anthropogenic Alter-

ation Development of an Offline Water QualityModel

Puget Sound, (or Salish Sea) a fjordal estuary in Washing-ton, has experienced water quality degradation in the formof harmful algal blooms and hypoxia in recent decades.Given climate change and sea level rise possibilities, thereis considerable interest in understanding the current andfuture effects of anthropogenic activities such as coastaldevelopment and nutrient loading on circulation and waterquality. An unstructured grid multi-scale model of PugetSound with a grid size capable of resolving small channelsnear river mouths to coastal open waters and accommo-dating complex shoreline geometry, waterways, and islandswas set up using finite volume coastal ocean model (FV-COM). To facilitate long-term water quality simulationsindependent of hydrodynamics, a companion offline waterlinkage code has been developed using FVCOM discretiza-tion of the study domain using biogeochemical kineticsfrom CE-QUAL-ICM model. A total of 19 state variablesare considered including two species of algae, dissolved andparticulate carbon, and nutrients, as part of the carbon cy-cle to calculate algal production and decay, and the impacton dissolved oxygen. Preliminary model application is pre-sented in the form of a sensitivity analysis to evaluate theeffect of alterations to nutrient loads, hydrologic loads, andsea level rise on circulation, and dissolved oxygen and al-gae growth. The effect of hydraulic modifications such asthe presence of a floating bridge on flushing time and wa-ter quality are also examined. The overall objective is toidentify whether human sources of nutrients in and aroundPuget Sound significantly impact ecosystem and if so howmuch nutrient reduction is necessary to improve ecologicalhealth in sensitive areas.

Tarang Khangaonkar,Pacific Northwest Laboratorytarang.khangaonkar@pnl.gov

Taeyun Kim, Zhaoqing YangPacific Northwest National Laboratorytaeyun.kim@pnl.gov, zhaoqing.yang@pnl.gov

MS32

Title Not Available at Time of Publication

Abstract not available at time of publication.

Ethan KubatkoDepartment of Civil and Environmental EngineeringThe Ohio State Universitykubatko.3@osu.edu

MS32

Storm Surge/Inundation Model Inter-Comparisonsvia a Super-Regional Test Bed on the U.S. Atlanticand Gulf of Mexico Coasts

Abstract not available at time of publication.

Rick LuettichUniversity of North Carolina - Moorehead Cityrick luettich@unc.edu

MS33

Designing a Top-down Inversion System AccurateEnough for Operational Use

With California law limiting greenhouse gas emissions

GS11 Abstracts 95

(AB32), policy makers will need emission estimates thatare much more accurate than are usually achieved by top-down methods. One particular challenge is that the math-ematical inversion techniques usually used assume that er-rors in the model and observations are unbiased. How-ever, we find that biases have a major impact on retrievedemissions. We also show how observation networks can beoptimized with respect to multiple constraints.

Philip Cameron-SmithLawrence Livermore National Laboratoriespjc@llnl.gov

Donald Lucas, Daniel BergmannLawrence Livermore National Laboratorylucas26@llnl.gov, bergmann1@llnl.gov

MS33

What Can We Learn About Fossil Fuel EmissionsAcross North America from a Geostatistical Atmo-spheric CO2 Inversion Using Ground-Based Con-tinuous Measurement Data?

Estimating anthropogenic CO2 emissions from variabil-ity in atmospheric CO2 concentrations requires separat-ing out the anthropogenic from the strongly varying bio-spheric signal. Without the use of expensive C14 mea-surements, atmospheric CO2 inversions can still providesome insight into the quality of inventory-based emissionestimates. This talk will present results from a geosta-tistical inversion over North America for 2004 and 2008using continuous ground-based measurement data and aLagrangian atmospheric transport model. This method isunique among inversion setups as it provides the opportu-nity to a) infer a set of total flux estimates that are com-pletely independent of any process-based model output,while b) gaining insight into the underlying processes, e.g.by correlating individual sectors from a fossil fuel inventorydatabase with estimated fluxes. The method can also beused to identify how consistent fossil fuel inventories arewith the atmospheric measurements at larger regions suchas state boundaries. Results also show how the expand-ing continental measurement network helps to further con-strain and isolate the fossil fuel emission signal across thecontinent, providing hope for future inversions that will usesatellite-based data for large regional anthropogenic CO2budgeting.

Sharon Gourdji, Kim Mueller, Vineet Yadav, AbhishekChatterjee, Deborah HuntzingerUniversity of Michigansgourdji@umich.edu, kimlm@umich.edu,vineety@umich.edu, abhishch@umich.edu,dnhuntzi@umich.edu

Arlyn AndrewsNOAA ESRLarlyn.andrews@noaa.gov

Anna MichalakUniversity of Michiganamichala@umich.edu

MS33

Impacts of Spatial and Temporal Correlations inRegional Atmospheric Inverse Estimates of Green-house Gas Fluxes

High-resolution inversions of greenhouse gas fluxes are sen-

sitive to treatment of spatial and temporal correlations. In-creasingly dense observations allow these correlations to beevaluated with more confidence. We present assessments ofthe spatial and temporal correlations in model-data differ-ences in atmospheric mixing ratios and surface fluxes. Weevaluate the importance of quantification of these correla-tions in flux estimates and uncertainty assessments, usingdata from North America and from the Midcontinent In-tensive.

Ken DavisPenn State Universitydavis@meteo.psu.edu

Timothy HiltonThe Pennsylvania State Universityhilton@meteo.psu.edu

Thomas Lauvauxtul5@meteo.psu.eduthe pennsylvania state university

Martha Butler, Liza Diaz, Klaus Keller, Natasha Miles,Scott RichardsonThe Pennsylvania State Universitympbulter@meteo.psu.edu, lzd120@psu.edu,kkeller@geosc.psu.edu, nmiles@meteo.psu.edu,srichardson@psu.edu

Arlyn AndrewsNOAA ESRLarlyn.andrews@noaa.gov

Nathan UrbanPrinceton Universitynurban@princeton.edu

MS33

Multiscale Spatial Models for Representing CO2

Emissions

While multi-Gaussian models have been successfully usedto represent biospheric CO2 emissions in inversion studies,it is less clear what models may apply for anthropogenicemissions. In this talk, we will explore various modelsthat employ easily observed covariates like GDP, popula-tion density etc to capture spatially variable anthropogenicCO2 emission. The dimensionality of the model will be ofparticular interest. The models will be tested using datafrom fossil-fuel emissions databases for North America.

Jaideep RaySandia National Laboratories, Livermore, CAjairay@sandia.gov

Sean McKennaSandia National LaboratoriesAlbuquerque, NMsamcken@sandia.gov

Bart G. Van Bloemen WaandersSandia National Laboratoriesbartv@sandia.gov

MS34

Advances in Tsunami Wave Propagation and Inun-

96 GS11 Abstracts

dation Modeling with Adaptive Triangular Meshes

Adaptive triangular meshes have proven their suitabilityfor representing complex bathymetry/topography featuresas well as multi-scale phenomena and interaction. Anadaptive tsunami propagation and inundation model usingGalerkin-type numerical approximations has been devel-oped and validated. In this presentation we introduce thenumerical method and show results of diverse simulations.It turns out that the adaptive mesh refinement improvescomputation time without sacrificing accuracy.

Joern BehrensKlimaCampus, University of Hamburgjoern.behrens@zmaw.de

MS34

An Adaptive Approach for the Propagation-Inundation Tsunami Problem

When dealing with geophysical problems we encountermulti-scale physical phenomena. A very actual exam-ple is the tsunami case where a hundred of kilometerscharacteristic-length waves travel trough the ocean to in-teract with meter-lengths scale coastal topography in theprocess of inundation. One possible approach to solve thefull problem is to discretize the physical domain with thesmaller scale resulting in a very inefficient computation dueto the over-resolved tsunami waves. Another possibilityis to subdivide the physical domain in several single-scaleproblems, solve the equations on each of them from thecoarser to the finer scale and connect them using bound-ary conditions. The problem with this approach is thatwe obtain a one-way communication pattern, from coarseto fine mesh, which can lead to inaccurate local solutions.We are working on solving the complete problem followingan adaptive approach. For spatial variability we adjust themesh resolution using unstructured meshes while for timevariability we use a local time step approach. We combinethese techniques with an high-order accurate finite volumenumerical method.

Cristobal E. CastroKlimaCampus, University of Hamburgcristobal.castro@zmaw.de

MS34

Tsunami Simulations with DGCOM: A High-orderTriangular Discontinuous Galerkin Coastal OceanModel

We describe the development of a triangular high-orderdiscontinuous Galerkin coastal ocean model that is beingdeveloped for modeling tsunamis. The model had previ-ously been used to study the 2004 Indian Ocean tsunamibut that version did not have wetting and drying al-gorithms. With wetting and drying algorithms now inplace, we can study the effects of this phenomenon on thestrengths of the tsunami waves and their impact on theshore lines. We will describe our wetting and drying al-gorithms and discuss extensions to high-order methods aswell as describe other types of high-order boundary condi-tions (such as non-reflecting types). Finally, we will dis-cuss the time-integration strategy being developed for thismodel including explicit, semi-implicit, and fully-implicittime-integrators.

Francis X. GiraldoNaval Postgraduate Schoolfxgirald@nps.edu

Shiva GopalakrishnanDepartment of Applied MathematicsNaval Postgraduate Schoolsgopalak@nps.edu

Dimitrios AlevrasHellenic Hydographic OrganizationAthens, Greecedimalevras@yahoo.com

MS34

Computational Challenges in Real-time TsunamiForecasting

The next generation tsunami forecast provides estimatesof all critical tsunami parameters (amplitudes, inundationdistances, current velocities etc.) based on direct tsunamiobservation and model predictions. There are significantchallenges in meeting Tsunami Warning Centers opera-tional requirements - speed, accuracy, and user interfacesthat provide guidance that is easy to interpret. Tsunamimodeling methods have matured into a robust technol-ogy that has proven to be capable of accurate simulationsof past tsunamis. However, implementing this technol-ogy into real-time tsunami forecast and warning operationspresents significant computational obstacles, including ac-cess to large model database, real-time data assimilation,real-time model runs etc. The methodology, tools, test re-sults, operational implementation and computational chal-lenges of the tsunami forecast system are discussed.

Vasily Titov

NOAA/Pacific Marine Environmental Laboratory7600 Sand Point Way NE, Bldg.3, Seattle, WA98115-6349vasily.titov@noaa.gov

MS34

Nonlinearity, Dispersion and Friction in TsunamiModeling

Abstract not available at time of publication.

Ahmet YalcinerMETU Department of Civil EngineeringOcean Engineering Research Center, 06531 AnkaraTurkeyyalciner@metu.edu.tr

MS35

Upscaling of Fine Scale Geological Models for Non-Linear Flow Simulations

The generalized Forchheimer law is considered for incom-pressible and slightly compressible flow filtration in porousmedia. The resulting system can be rewritten in term ofnon-linear equations for the pressure only, characterized bythe permeability tensor depending on the pressure gradientnorm. In this work we explore the possibility of extendingsome of the local and extended local linear Darcy upscal-ing models to the non-linear Forchheimer law. Coarse scalesimulation results are presented.

Akif Ibragimov, Eugenio AulisaDepartment of Mathematics and Statistics.Texas Tech Universityakif.ibraguimov@ttu.edu, eugenio.aulisa@ttu.edu

GS11 Abstracts 97

MS35

Uncertainty Quantification for Subsurface FlowProblems using Coarse-scale Models

Uncertainty quantification for subsurface flow often re-quires flow simulation on multiple geological models. Wepresent an upscaling approach that entails statistical as-signment of upscaled functions, and rapidly generates thosefunctions for multiple models. The goal is to reproduce theensemble statistics (e.g., P50, P10 and P90) of the fine-scale flow. This differs from most existing upscaling tech-niques, in which the intent is to reproduce the fine-scalesolutions on a realization-by-realization basis.

Yuguang ChenChevron Energy Technology CompanyYChen@chevron.com

MS35

An Eulerian Joint Velocity-concentration PDFMethod for Solute Dispersion in Highly Hetero-geneous Porous Media

In risk analysis applications involving solute dispersion inheterogeneous formations, the knowledge of the concentra-tion probability density function (PDF) at different spa-tial locations and times is crucial. A new joint velocity-concentration PDF method is proposed that is applicablefor highly heterogeneous porous media. The correspondingPDF transport equation accounts for advective transport,pore-scale dispersion, molecular diffusion, and chemical re-actions. It is solved numerically using an efficient particle-based approach.

Daniel W. MeyerInstitute of Fluid Dynamicsmeyerda@ethz.ch

Patrick JennyInstitute of Fluid DynamicsETH-Zentrumjenny@ifd.mavt.ethz.ch

Hamdi TchelepiPetroleum Engineering DepartmentStanford Universitytchelepi@stanford.edu

MS35

Adaptive Error Control in the Multiscale FiniteVolume Method for Multiphase Flow in PorousMedia

The iterative MSFV method is extended to include the se-quential fully implicit simulation of time dependent prob-lems that involves a system of pressure-saturation equa-tions. To control numerical errors in simulation results,an error estimate, based on the residual of the MSFV ap-proximate pressure field, is introduced. In the initial timestep in simulation, iteration is employed until a specifiedaccuracy in pressure solution is achieved. This initial so-lution is then utilized to improve the localization assump-tion of basis functions at later time steps. Additional it-erations in pressure solution are employed only when thepressure residual becomes larger than a specified thresh-old value. A priori error estimate and control based onpressure-equation residuals are derived to guarantee thedesired numerical accuracy in saturation solution. Effi-ciency of the adaptive iteration strategy and error control

criteria are also numerically examined.

Seong H. LeeChevron ETCSEON@chevron.com

Hadi HajibeygiInstitute of Fluid DynamicsETH Zurichhajibeygi@ifd.mavt.ethz.ch

Ivan LunatiUniversity of Lausanneivan.lunati@unil.ch

MS36

Modelling of Biofilm Growth and its Influence onCO2 and Water (two-phase) Flow in Porous Media

With the aim of aiding experimental design and for feasi-bility studies, a numerical model is developed capable ofsimulating the precipitation of calcite in sand or rock sam-ples due to the activity of ureolytic bacteria. The model,which is defined on the Darcy scale, accounts for the accu-mulation of biofilms, their influence on pH, and the sub-sequent changes in the properties of the porous medium.

Rainer HelmigIWS, University of Stuttgart, GermanyInstitut fur Wasserbaurainer.helmig@iws.uni-stuttgart.de

MS36

Gas Invasion in Soft Sediments

We investigate the displacement of one fluid by another ina deformable medium with pore-scale disorder. We developa model that captures the dynamic pressure redistributionat the invasion front, and the feeback between fluid inva-sion and microstructure rearrangement. Our results sug-gest how to collapse the transition between invasion per-colation and viscous fingering in the presence of quencheddisorder. We predict the emergence of a fracturing patternfor sufficiently deformable media, in agreement with obser-vations of drainage in granular material, and we identify adimensionless number that appears to govern the crossoverfrom fingering to fracturing.

Ran Holtzman, Ruben JuanesMITCivil and Environmental Engineeringrholtzman@mit.edu, juanes@mit.edu

MS36

Sniffing for Leakage: Trace Gas Sensors and Car-bon Sequestration

Trace gas sensors are based on optothermal detection anduse a modulated laser source and a quartz tuning fork am-plifier to detect small amounts of gases for disease diag-nosis via breath analysis and monitoring of atmosphericpollutants and greenhouse gases. We introduce the firstmathematical model of a resonant optothermoacoustic sen-sor. The model is solved via the finite element method andcouples heat transfer and thermoelastic deformation to de-

98 GS11 Abstracts

termine the strength of the generated signal.

Susan E. MinkoffUniversity of Maryland, Baltimore CountyDept of Mathematics and Statisticssminkoff@umbc.edu

Noemi PetraInstitute for Computational Engineering and SciencesUniversity of Texas at Austinnoemi@ices.utexas.edu

John W. ZweckUniversity of Maryland Baltimore CountyMathematics and Statisticszweck@umbc.edu

Anatoliy Kosterev, James DotyDepartment of Electrical and Computer EngineeringRice Universityakoster@rice.edu, jim.doty@rice.edu

MS36

Role of Guest Molecule Exchange Kinetics on theInjectivity of Liquid CO2 into Gas Hydrate BearingFormations

Geologic accumulations of natural gas hydrates hold vastorganic carbon reserves, potentially meeting global energyneeds for decades. The principal challenge for this uncon-ventional energy resources is to develop production tech-nologies that minimize energy costs and environmental im-pacts. The CO2-CH4 guest molecule exchange technologyhold promise in this regard. Previous numerical simula-tions using an equilibrium approach predict pore pluggingupon injecting of CO2. This numerical study considers theimpact of exchange kinetics on formation injectivity.

Mark D. WhitePacific Northwest National Laboratorymark.white@pnl.gov

MS37

Simulation of Transport in 2D HeterogeneousPorous Media via a Random Walk Particle Track-ing method

We study the transport of an inert species in a 2D het-erogeneous porous medium via a Random Walk ParticleTracking (RWPT) method. The main objective is to derivethe macroscopic properties of the transport by the meansof Monte-Carlo simulations in large domains. Conditionsto reach asymptotic macro-dispersion coefficients will begiven. We will also present our on-going research aboutthe RWPT method in presence of discontinuities withinthe domain.

Geraldine PichotEquipe SAGEINRIA Rennes Bretagne Atlantiquegeraldine.pichot@inria.fr

Anthony BeaudoinInstitut PprimeUniversite de Poitiersanthony.beaudoin@univ-poitiers.fr

Nadir Soualem

Equipe SAGEINRIA Rennes Bretagne Atlantiquenadir.soualem@irisa.fr

Jocelyne ErhelINRIA-Rennes, FranceCampus de BeaulieuJocelyne.Erhel@inria.fr

Jean-Raynald de DreuzyGeosciences Rennes, UMR6118 CNRSUniversite de Rennes 1jean-raynald.de-dreuzy@univ-rennes1.fr

Michel KernINRIAmichel.kern@inria.fr

MS37

Flow and Mechanics in Discrete Fracture-matrixRock Systems: Hydromechanical Behavior Utiliz-ing an Extended Finite Element Method

This study aims to develop a fully coupled hydromechani-cal model which can more easily treat complex fracture ge-ometries. Our proposed method is based on the extendedfinite element method (XFEM) to represent fractures aslower dimensional elements for mechanics and solve a cou-pled problem in a monolithic manner. It can improve fea-sibility for meshing and nonlinear analysis. Our numericalstudy shows the proposed method can produce very similarresults to the interface element approach.

Norihiro WatanabeDepartment of Environmental InformaticsHelmholtz Centre for Environmental Research - UFZnorihiro.watanabe@ufz.de

Wenqing WangDepartment of Environmental InformaticsHelmholtz Centre for Environmental Researchwenqing.wang@ufz.de

Joshua TaronUFZjoshua.taron@ufz.de

Olaf KolditzHelmholtz Centre for Environmental Researcholaf.kolditz@ufz.de

MS37

PDF Methods for Uncertainty Quantification.

We obtain the probability density function (PDF) of thedistribution of a passive scalar that diffuses in a randomvelocity field. We derive an explicit map between the veloc-ity distribution and the scalar PDF, and determine exactsolutions for the PDF of the normalized scalar. This allowsfor the explicit quantification of the impact of diffusion onthe evolution of the scalar PDF without recurrence to aclosure approximation in terms of a mixing model.

Daniel M. TartakovksyUniversity of California, San Diegodmt@ucsd.edu

Marco Dentz

GS11 Abstracts 99

IDAEASpanish National Research Council (CSIC)marco.dentz@idaea.csic.es

MS37

Numerical Issues of Two-phase Flows in Heteroge-neous Media with Full Permeability Tensor

We consider the water flooding stage of oil recovery whenwater is injected into injection wells and pushes oil towardthe production wells. We discuss two numerical issuesof modeling two-phase immiscible flow in heterogeneousporous media with jumping anisotropic permeability ten-sor. The first issue is the effect of the discrete flux approx-imation on the front behavior and the water breakthroughtime. The second issue is the choice of the efficient solverfor algebraic systems produced by the simulator.

Yuri VassilevskiInstitute of Numerical MathematicsRussian Academy of Sciencesyuri.vassilevski@gmail.com

Ivan KapyrinRussian Academy of Sciencesivan.kapyrin@gmail.com

Kirill Nikitin, Aleksander DanilovInstitute of Numerical MathematicsRussian Academy of Sciencesnikitin.kira@gmail.com, a.a.danilov@gmail.com

MS38

Tetrahedral Mesh Generation for Reservoir Simu-lations; Barriers and Opportunities

The challenges and opportunities of using tetrahedralmeshes as reservoir simulation grids is investigated. Incontrast to the current industry practices of using cornerpoint grids, tetrahedral meshes are capable of representingmulti-scale geological features efficiently in a completelyautomated way. The use of these grids opens many oppor-tunities for building a reservoir simulator that uses mixedhigher order numerical schemes on the tetrahedral gridsand the dual control volumes.

Ahmed H. ElSheikh, Jefferson Gomes, Matthew JacksonDepartment of Earth Science and EngineeringImperial College London, South Kensington Campusa.el-sheikh@imperial.ac.uk, j.gomes@imperial.ac.uk,m.d.jackson@imperial.ac.uk

Tara LaForceImperial College Londont.laforce@imperial.ac.uk

Gerard GormanDepartment of Earth Science and EngineeringImperial College London, South Kensington Campusg.gorman@imperial.ac.uk

Chris PainImperial Collegec.pain@imperial.ac.uk

MS38

Impact of Geological Uncertainty and Simulation

Method in CO2 Storage

Deep saline aquifers hold great capacity for CO2 geose-questration but also have great uncertainty. StreamlineSimulations are ideal for fast simulation, as complex 3Dsystems are divided into 1D problems. We combine com-pressibility and a new phase behaviour algorithm in oursimulator, which improves convergence without additionalcomputational cost. Simulations on 10 geological realisa-tions following a Huff-and-Puff injection scheme (OtwayProject) are compared with an industrial simulator withresults of 80% of CO2 rendered immobile.

Lorena Lazaro Vallejo, Tara LaForceImperial College Londonlorena.lazaro@imperial.ac.uk, t.laforce@imperial.ac.uk

MS38

Microporosity Characterization and Representa-tive 3D Modeling of Tight Gas Sandstones

Accurate representation of geometry has the first order in-fluence on multiphase fluid flow in porous media on allrelevant scales. Existing pore scale network flow modelsthat successfully model granular materials and sandstonesof porosity <= 0.1 do not capture capillary-pressure behav-ior characteristic of many tight gas sandstones. We presentan image based characterization of microporosity, crucialfor tight porous media, as well as how to incorporate it intoa 3D model.

Masa ProdanovicUniversity of Texas at AustinDepartment of Petroleum and Geosystems Engineeringmasha@ices.utexas.edu

Peter EichhublUniversity of Texas at Austinpeter.eichhubl@beg.utexas.edu

Steven BryantDepartment of Petroleum and Geosystems EngineeringInstitute for Computational and Engineering Sciencessteven bryant@mail.utexas.edu

Edward Wanat, J. Steven DavisExxonMobil Upstream Research Companyedward.c.wanat@exxonmobil.com,j.steve.davis@exxonmobil.com

MS38

Mortar Coupling of Pore-scale Models to ReservoirSimulators; a True Multiscale Approach

Pore-scale models are useful tools for estimating macro-scopic parameters (e.g., permeability), but direct upscal-ing could result in misleading values, partly because em-ployed boundary conditions ignore the impact of surround-ing media. Here, we develop a novel multiscale simulator,where pore-scale models are coupled directly with contin-uum scale models. Continuity of pressures and fluxes areenforced at shared boundaries using finite element mortars.Moreover, we develop priori upscaling techniques that al-low for fast coupling between pore-scale models.

Tie SunUniversity of Texas at Austinsun.tie@mail.utexas.edu

100 GS11 Abstracts

Matthew BalhoffThe University of Texas at AustinDepartment of Petroleum and Geosystems Engineeringbalhoff@mail.utexas.edu

Yashar MehmaniThe University of Texas at Austinyashar.mehmani@gmail.com

MS39

Multiscale Mortar Methods for Flow in Heteroge-neous Porous Media

We consider a second order elliptic problem with a het-erogeneous coefficient written in mixed form. We view thedomain decomposition method as a multiscale method withrestricted degrees of freedom on the interfaces. We devisean effective but purely local multiscale method that in-corporates information from homogenization theory. Wealso use this decomposition method approach to devise ef-fective preconditioners that incorporate exact coarse-scaleinformation to iteratively solve the full fine-scale problem.

Todd ArbogastDept of Math; C1200University of Texas, Austinarbogast@ices.utexas.edu

Hailong XiaoICESThe University of Texas at Austinxiaohl@ices.utexas.edu

MS39

Multiscale Mixed FEM for Compressible Flow

Multiscale methods have been shown to be a robust andaccurate alternative to traditional upscaling methods forincompressible flow. We discuss the extension of a multi-scale mixed method to compressible flow, using more thanone basis function for each coarse face and a residual for-mulation with a domain-decomposition corrector.

Knut-Andreas LieSINTEF ICT, Dept. Applied MathematicsKnut-Andreas.Lie@sintef.no

MS39

Mixed Multiscale Finite Volume Methods for Mod-eling of Fluid Flow in Porous Media

We develop a framework for constructing mixed multiscalefinite volume methods for flows in porous media. Someof the methods developed using the framework are alreadyknown; others are new. New insight is gained for the knownmethods and extra flexibility is provided by the new meth-ods. This method uses novel multiscale velocity basis func-tions that are suited for using global information, which isoften needed to improve the accuracy of the multiscale sim-ulations in the case of continuum scales with strong non-local features. The method efficiently captures the smalleffects on a coarse grid. We analyze the new mixed MsFVand apply it to solve two-phase flow equations in heteroge-neous porous media. Numerical examples demonstrate theaccuracy and efficiency of the proposed method for mod-eling the flows in porous media with non-separable and

separable scales.

Ilya D. MishevExxonMobil Upstream Research CompanyDepartment Technical Software Developmentilya.d.mishev@exxonmobil.com

Lijiang JiangIMA, University of Minnesotaljjiang@math.tamu.edu

MS39

Multiscale Mortar Multipoint Flux Mixed FiniteElement Methods for Flow in Porous Media

We develop a multiscale mortar multipoint flux mixed finiteelement method for flow in porous media. The equationsin the coarse elements are discretized on a fine grid scaleby a multipoint flux mixed finite element method that re-duces to cell-centered finite differences on irregular grids.The subdomain grids do not have to match across the in-terfaces. Continuity of flux between coarse elements is im-posed via a mortar finite element space on a coarse gridscale. With an appropriate choice of polynomial degree ofthe mortar space, we derive optimal order convergence onthe fine scale for both the multiscale pressure and velocity,as well as the coarse scale mortar pressure. The algebraicsystem is reduced via a non-overlapping domain decom-position to a coarse scale mortar interface problem thatis solved using a multiscale flux basis. Numerical exper-iments are presented to confirm the theory and illustratethe efficiency and flexibility of the method.

Mary F. WheelerCenter for Subsurface ModelingUniversity of Texas at Austinmfw@ices.utexas.edu

Guangri XueInstitute for Computational Engineering and SciencesUniversity of Texas at Austingxue@ices.utexas.edu

Ivan YotovUniveristy of PittsburghDepartment of Mathematicsyotov@math.pitt.edu

MS40

The Open Porous Media Initiative

The Open Porous Media Initiative aims to produce a widerange of simulators for porous media applications. Prin-cipal goals include the ability to model relevant industrialscenarios, easy extensibility, high performance and ease ofuse. The software uses the DUNE framework, yet effort ismade to ensure the reusability of the code within other con-texts. Initial work at SINTEF and IRIS has concentratedon simulation of petroleum reserviors. We present an ini-tial black-oil reservoir simulator and review its capabilites.

Kristin FlornesIRIS, Bergen, NorwayKristin.Flornes@iris.no

Atgeirr RasmussenSINTEF, Oslo, Norwayatgeirr@sintef.no

GS11 Abstracts 101

MS40

Our Software Commons and Where We Can MakeIt Lead Us

The global geoscience community is building a new, open,software toolbox. Instead of parochial, esoteric, highly-customized and under-maintained applications, we are see-ing the development of user-friendly platforms, maintainedby diverse and geographically widespread groups of aca-demics and professionals. The opportunities are grow-ing for collaborative innovation, spontaneous investigation,and just plain old fun. To realize this Arcadian dream, thecommunity must learn to value openness, nurture the skillsto contribute, and embrace new business models.

Matt HallConocoPhillipsmatt.hall@conocophillips.com

MS40

The Distributed and Unified Numerics Environ-ment DUNE and its Application to Porous Mediawith DuMuX

The first part presents DUNE, the Distributed and Uni-fied Numerics Environment, a modular toolbox for solv-ing partial differential equations (PDEs) with grid-basedmethods. The underlying idea of DUNE is to create sliminterfaces allowing an efficient use of legacy and/or new li-braries. The second part provides an overview of DuMux,a DUNE-based module for multi-{phase, component, scale,physics, ...} flow and transport in porous media.

Steffen MuthingInstitute of Parallel and Distributed SystemsUniversity of Stuttgartsteffen.muething@ipvs.uni-stuttgart.de

Bernd FlemischUniversity of Stuttgart, Germanybernd.flemisch@iws.uni-stuttgart.de

MS40

MATLAB Reservoir Simulation Toolbox

The MATLAB Reservoir Simulation Toolbox provides acomprehensive set of routines for developing and interac-tively studying simulation methods for porous media flowon unstructured grids. Emphasising flexibility and gener-ality with respect to grid formats, particularly supportinghierarchical grids in multiscale methods, MRST promotesresearch and computational experiments on realistic mod-els. Moreover, being open-source results and frameworksare accessible to anyone who wishes to reproduce or extendthe existing work.

Bard SkaflestadSINTEF, Oslo, Norwaybard.skaflestad@sintef.no

MS41

Free Surface Flows Modeling of Real Problems:The Electricit-De-France Point of View

Modeling free surface flows is one of the most challeng-ing areas for EDF. For its own applications, EDF devel-ops 1D and 2D numerical tools (Telemac and Mascaret)based on the shallow-water equations (SWE). Last devel-

opments focus, on one hand, on new numerical scheme (ki-netic schemes), and on the other hand, on the validity ex-tension of the classical SWE system for the 1D model byadding specific source terms. Industrial applications willillustrate these developments.

Riadh AtaEDF R&Driadh.ata@edf.fr

Nicole GoutalEDF R&D & Saint-Venant Hydraulic Lab.nicole.goutal@edf.fr

jacques sainte-marieINRIA & Saint-Venant Hydraulic Lab.jacques.sainte-marie@inria.fr

MS41

Immersed Boundary Method for Flood Simulation

Failure of dams and levees may lead to catastrophic floodsthat would cause loss-of-life and damage to urban and ru-ral areas. In this talk we describe a two-dimensional floodmodel based on a first order explicit scheme in which animmersed boundary technique is used to simulate linearterrain features that cannot be captured by the resolutionof the structured computational grid. The cut-cell bound-ary method is also used for providing coupled 1D-2D sim-ulation capability.

Mustafa Altinakar, Marcus McGrathNCCHE - University of Mississippialtinakar@ncche.olemiss.edu,mzmcgrat@ncche.olemiss.edu

Edie Miglio

Politecnico di Milano (Italy)MOX, Dept. of Mathematicsedie.miglio@polimi.it

MS41

High-resolution Modeling of Urban Dam-breakFlooding

Here, we present a modeling study of the Baldwin Hillsdam-break flood (Los-Angeles 1963), whereby inundationis resolved at a spatial and temporal scale of ca. 3 m and0.1 s, respectively. The ability of the model to correctlypredict flood extent and streamflow is reported, model sen-sitivities are examined, and the potential to predict damagezones is discussed. The results of this study point to a newparadigm for urban dam-break flood impact analyses.

brett SandersUniverity of California, Irvinebsanders@uci.edu

Jochen ShubertThe University of Nottinghamjochen.schubert@nottingham.ac.uk

humberto GallegosUniverity of California, Irvinegallegos@uci.edu

102 GS11 Abstracts

MS41

Improvement of the Flood Simulation with MAS-CARET using Data Assimilation

A data assimilation procedure was implemented on top ofthe mono-dimensional hydraulics model MASCARET. Theprocedure is two-fold: the BLUE algorithm is used to as-similate river water level observations to correct the up-stream flow forcing and also to instantaneously correct thewater level and discharge. It was shown over a significantnumber of flood events for the Adour catchment that thetwo-step data-assimilation procedure improves the simula-tion in re-analysis and forecast modes

Sophie ricci, olivier ThualCERFACSricci@cerfacs.fr, thual.o@gmail.com

MS42

Simulations of a Field of Precipitating Trade-windCumuli using a Particle-based and ProbabilisticMicrophysics Model Coupled with LES: ModelingResults and Validation against in-cloud AircraftObservations

We present results of LES modeling of a field of shallowconvective maritime clouds using the so-called RICO set-up (van Zanten et. al, submitted to J. Adv. Model.Earth Syst., 2010). We use the Super Droplet Method(Shima et al., Quart. J. Roy. Meteor. Soc., 2009) forcoupling the non-hydrostatic LES CReSS (Tsuboki andSakakibara, Quart. J. Roy. Meteor. Soc., 2006) withparticle- based simulation resolving explicitly such cloud-microphysical processes as CCN activation, condensationaland collisional growth growth of cloud droplets and gravi-tational sedimentation including drizzle and rain precipita-tion. Model results are compared with simulations employ-ing bulk treatment of cloud microphysics as well as withaircraft observations of cloud-droplet size spectrum duringthe RICO experiment (Arabas et al., Geophys. Res. Lett.,2009).

Sylwester J. ArabasInstitute of GeophysicsUniversity of Warsaw, Polandsarabas@igf.fuw.edu.pl

Shin-ichiro ShimaThe Earth Simulator Center (ESC), Japan Agency forMarine-Earth Science and Technology (JAMSTEC), Yokohama,JAPANs shima@jamstec.go.jp

MS42

Multiscaling and Approximations for CoagulationProcesses in High Dimension

Computing the time evolution of the multi-dimensional sizedistribution of atmospheric aerosol particles involves manycomputational subcomponents, and one of the more com-putationally intense of these is computing the effect of co-agulations amongst particles. In this talk, we will discussseveral methods of speeding up particle methods by ex-ploiting the multiple timescales in many coagulation sce-narios.

Lee DeVilleUniversity of Illinois

Department of Mathematicsrdeville@math.uiuc.edu

MS42

Simulating Multivariate Particle Populations bythe Quadrature Method of Moments (QMOM)

The method of moments (MOM) offers a statistically basedapproach that tracks only the moments of a multivariateparticle population. This makes the method highly effi-cient. The introduction of quadrature in the QMOM givesboth closure of the moment evolution equations and ex-cellent approximation to distribution properties (physical,optical, etc.) in terms of moments. As one example of theapproach we use particle-resolved simulations of Riemer etal. [JGR, 2009] to benchmark QMOM accuracy during abi-variate simulation of the mixing states of soot and sul-fate particles undergoing coagulation. This important “ag-ing” mechanism determines aerosol optical properties andcloud condensation nuclei (CCN) concentrations in the at-mosphere. Several different quadrature schemes are tested.Gauss and Gauss-Radau quadratures appear to give nestedlower and upper bounds, respectively, to aerosol mixingrate. Similarities between the QMOM and Kalman filter-ing will also be discussed.

Robert McGrawAtmospheric Sciences DivisionBrookhaven National Labrlm@bnl.gov

MS42

Parallel Particle Methods for Aerosol Simulation

Particle-resolved stochastic models offer unprecedentedlevels of detail for aerosol dynamics, but at the ex-pense of increased computational cost. To enable fastparticle-resolved simulation we present several paralleliza-tion strategies, including local mixing-based algorithmsand global particle-request methods, and compare theirperformance and scaling. All of the parallel algorithmsconsidered are approximate, but we prove convergence tothe centralized case in appropriate limits.

Matthew WestMechanical Science and EngineeringUniversity of Illinois at Urbana-Champaignmwest@illinois.edu

MS43

A Space-Filling-Curve Approach for Parallel Adap-tive Mesh Refinement in Tsunami Simulaton

Efficient parallel adaptive refinement (AMR), to captureland-ocean boundaries and to dynamically refine alongpropagating wave-fronts, is a performance-critical compo-nent of Tsunami simulation. We present a respective ap-proach for parallel AMR and respective solvers for systemsof PDE that is based on recursively structured adaptive tri-angular grids and corresponding element orders using Sier-pinki space-filling curves. The approach allows for perfor-mance optimisation w.r.t multiple aspects: minimal mem-ory requirement, inherently cache efficient processing, aswell as fast load balancing. Test results are presented for asimple discontinuous Galerkin solver for the shallow waterequations.

Michael Bader, Kaveh RahnemaUniversity of Stuttgart

GS11 Abstracts 103

Institute of Parallel and Distributed SystemsMichael.Bader@ipvs.uni-stuttgart.de,kaveh.rahnema@ipvs.uni-stuttgart.de

Csaba VighInstitut fur InformatikTU Munchen, Germanyvigh@in.tum.de

MS43

Seismic Inversion using Discontinuous GalerkinMethods

We present aspectral-element-based Discontinuous Galerkin method todiscretize full wave form seismic inverse problems. The in-verse problem is formulated in a Bayesian framework, and adiscretize-then-optimize approach is used to derive the gra-dient and Hessian-vector product. A result on the equiva-lence between discretize-then-optimize and optimize-then-discretize will be presented. Finally, primarily results onfull wave Bayesian inversion on massive parallel computersdemonstrate the capabilities of our approach.

Tan Bui-Thanh, Carsten BursteddeThe University of Texas at Austintanbui@ices.utexas.edu, carsten@ices.utexas.edu

Omar Ghattas, Georg Stadler, Lucas WilcoxUniversity of Texas at Austinomar@ices.utexas.edu, georgst@ices.utexas.edu,lucasw@ices.utexas.edu

MS43

Tsunami Edge Waves and Complex EarthquakeRupture

Edge waves are a particular type of coastal wave trapped byrefraction that propagate parallel to the coastline. In com-bination with scattering and resonance, edge waves create acomplex waveform in which the offshore amplitude, runup,and timing of the largest wave are difficult to predict usingstandard numerical methods. Instead, edge waves fromcontinental-shelf tsunamis, such as the 2010 Chile event,are examined from an analytic perspective and in relationto complex rupture models.

Eric L. GeistUS Geological Surveyegeist@usgs.gov

MS43

Efficient Local Resorting Techniques with SpaceFilling Curves Applied to a Parallel Tsunami Sim-ulation Model

The OpenMP-parallel model TsunAWI for the simulationof tsunami propagation and inundation discretizes the shal-low water equations on an unstructured P1−P NC

1 finite ele-ment grid. The data access to the variables on the unstruc-tured grid is crucial for the computational performance. Areordering of the unknowns at elements, nodes, and edgesalong a space filling curve is presented that guarantees datalocality on all levels of the memory hierarchy, thus reducingcash misses and false sharing.

Natalja RakowskyAlfred-Wegener-Institute for Polar and Marine Research

Am Handelshafen 12, 27570 Bremerhaven, Germanynatalja.rakowsky@awi.de

Annika FuchsAlfred-Wegener-Institute for Polar and Marineannika.fuchs@awi.de

MS44

New Mathematical Models and Numerical Simula-tions of Multiphase Flows in Porous Media Includ-ing Phase Transitions and Chemical Reactions

Abstract not available at time of publication.

Karl Heinz HoffmannPhysics InstituteTechnical University of Chemnihoffmann@physik.tu-chemnitz.de

MS44

Time-relaxation Methods for Degenerate Trans-port Problems

In this talk, we discuss the application of time-relaxationmethods for degenerate transport problem. The work ismotivated by regions in the subsurface where the governingequations change type from hyperbolic to parabolic. Thisoccurs, for instance, when fronts move through the un-saturated zone or when material parameters change. Ourfindings indicate that can improve results obtained from afinite difference or continuous FEM scheme by applying asimple elliptic operator. We give theoretical and numericalevidence to support the use of these operators in legacycodes.

Lea JenkinsDepartment of Mathematical SciencesClemson Universitylea@clemson.edu

MS44

A Physics-based Sparsified Solver for ReservoirSimulation

In the present work we propose a percolation-based sparsi-fication algorithm to solve pressure-based systems arisingin porous media flow applications. The main idea of thisphysics-based strategy is to capture the connectivity lay-out or solution paths describing the overall flow processon highly heterogeneous media. The proposed approachhas the potential to mitigate the overhead associated withpreconditioner construction and application. Results areillustrated on a wide set of field cases arising in black-oiland compositional simulations.

Hector KlieConocoPhillips CompanyHector.M.Klie@conocophillips.com

MS44

A Dirichlet-to-Neumann Multigrid Algorithm forLocally Conservative Methods

Discontinuous Galerkin methods and mixed finite elementmethods have grown in popularity in recent years withrecent work showing that both methods give rise to lo-cally conservative fluxes. In this talk we introduce a novel,physics-based geometric multigrid framework that incorpo-

104 GS11 Abstracts

rates both mixed and DG with optimal convergence prop-erties even in the case of multinumerics and unstructuredgrids. Theoretical results for symmetric operators will bepresented along with numerical results for the both sym-metric and nonsymmetric problems.

Tim M. WildeyThe University of Texas at AustinAustin, USAtwildey@ices.utexas.edu

Mary F. WheelerCenter for Subsurface ModelingUniversity of Texas at Austinmfw@ices.utexas.edu

MS45

Complex Evolution of Transport Properties in CO2

Infiltrated Coal: Observations and Models

We explore the evolution of permeability in coal withswelling-induced sorption of single and multi-componentgases such as CO2, CH4, N2 relative to non-sorbing He.We explore important differences in the sense and timing ofpermeability evolution in porous coals, ubiquitously frac-tured coals and in coals containing a distribution of flaws.We extend these models to follow permeability evolutionin coals infiltrated by binary mixtures through the appli-cation of distributed parameter models.

Derek ElsworthPenn State Universityelsworth@psu.edu

Shugang Wang, Ghazal Izadi, Hemant KumarEnergy and Mineral EngineeringPenn State Universityszw138@psu.edu, gui2@psu.edu, huk145@psu.edu

Jishan Liu, Zhongwei ChenMechanical EngineeringUniversity of Western Australiajishan@mech.uwa.edu.au, zhongwei@mech.uwa.edu.au

Jonathan MathewsEnergy and Mineral EngineeringPenn State Universityjpm10@psu.edu

Denis PoneConocoPhillipsdenis.pone@conocophillips.com

MS45

Non-isothermal Flows in Porous Media for CO2 Se-questration Applications

Non-isothermal flows in porous media for CO2 sequestra-tion applications Norbert Bttcher, Ashok Singh, Chan-HeePark, Wenqing Wang, Joshua Taron, Uwe Grke and OlafKolditz Abstract: This paper deals with non-isothermalflow effects during carbon dioxide sequestration. We con-sider two scenarios: (i) the miscible displacement of com-pressible natural gases through a layer of the depleted gasreservoir by injection of carbon dioxide and (ii) CO2 se-questration in deep saline aquifers. We consider the realbehavior of gaseous mixtures and immiscible fluids throughusing energy and distance parameters in the calculation of

material parameters. In this situation dispersive mass-fluxis often more significant than diffusive processes. We usethe empirically extended ideal gas equation to calculate thedensity for mixtures. Gas injection to reservoirs can causere-pressurization effects and reservoir temperature can fallsignificantly according to the Joule - Thomson cooling ef-fect. The energy conservation equation is solved to accountfor heat loss due to gas expansion and viscous heat dissipa-tion. In two-phase flow systems density dependent effectshave to be considered in addition.

Norbert BottcherTU Dresdennorbert.boettcher@tu-dresden.de

Ashok SinghUFZashok.singh@ufz.de

Chan-Hee ParkKIGAMchanhee.park@kigam.re.kr

Wenqing WangDepartment of Environmental InformaticsHelmholtz Centre for Environmental Researchwenqing.wang@ufz.de

Joshua Taron, Uwe GorkeUFZjoshua.taron@ufz.de, uwe-jens.goerke@ufz.de

Olaf KolditzHelmholtz Centre for Environmental Researcholaf.kolditz@ufz.de

MS45

Multiscale Modeling in the Context of CO2 Storage

The disparity between laboratory scales and the scaleneeded for CO2 storage to be meaningful, makes upscal-ing and simulation central research components. Here, welook at how coupled physical phenomena impact models atdifferent scales. In particular, we emphasize how the repre-sentation of physical processes changes on different scaleswithin a coupled model.

Jan M. NordbottenDepartment of MathematicsUniversity of Bergenjan.nordbotten@math.uib.no

MS45

Modeling the Complex Evolution of FracturedGeothermal Reservoirs

We develop models for the evolution of fractured geother-mal reservoirs where mechanical and chemical responsesare innately linked. The linkage between mechanics andchemistry is shown to progress at a variety of differenttimescales depending on diffusional control of the pro-cesses. Effective stress effects are immediate, followed byshort-term thermal drawdown and the development of hy-droshears. The final stage of evolution involves chemicalinfluences and their effect of the hydraulic performance ofthe reservoir.

Joshua Taron

GS11 Abstracts 105

UFZjoshua.taron@ufz.de

Derek ElsworthPenn State Universityelsworth@psu.edu

Baisheng Zheng, Ghazal IzadiEnergy and Mineral EngineeringPenn State Universitybzz105@psu.edu, gui2@psu.edu

MS46

Anomalous Transport in Heterogeneous Media:Broad Heterogeneity Distributions Versus StrongHeterogeneity Correlations

We study mechanisms that can lead to anomalous trans-port in quenched random media. Broad disorder point dis-tributions and strong disorder correlations cause anoma-lous transport and can lead to the same anomalous scal-ing laws for the centered mean and mean squared particledisplacements. The respective mechanisms, however, arefundamentally different. This difference is reflected in thespatial particle densities and first passage time distribu-tions, which provide indicators for identifying the originsof anomalous transport.

Marco DentzIDAEASpanish National Research Council (CSIC)marco.dentz@idaea.csic.es

Diogo BolsterUniversity of Notre Damediogobolster@gmail.com

MS46

Multiscale Finite Elements Methods for High Con-trast Diffusion Problems

We discuss multiscale finite element methods for ellipticproblems with high contrast coefficients, arising in flow ina heterogeneous porous medium. For a restricted class ofmodel problems our method has optimal convergence, in-dependent of the geometry and contrast of the PDE coef-ficient. We also present an adaptive variant of the methodwhich can be applied to rather general flow problems withsimilar convergence properties. Experiments on a widerange of model problems are presented.

Ivan G. GrahamUniversity of BathI.G.Graham@bath.ac.uk

Ray MillwardDept of Mathematical SciencesUniversity of Bathr.r.millward@bath.ac.uk

MS46

Numerical Simulation of Reactive Transport: Ap-plication to CO2 Storage in Heterogeneous Media

Coupling transport with geochemistry adds chemical het-erogeneity as a new difficulty to the simulation of flow andtransport in porous media. Reactive phenomena, such asprecipitation or dissolution of minerals, are usually highly

localized in space, and this in turn requires very accuratesimulation codes, as well as an accurate coupling algorithm.The Newton-Krylov method is a globally coupled approachthat is both robust and accurate. We apply the method, toa system including mineral reactions and gas dissolution,that is relevant to CO2 storage.

Blandine GueslinCRI Paris RocquencourtINRIA Franceblandine.gueslin@inria.fr

Michel KernINRIAmichel.kern@inria.fr

MS47

An Experimental Approach using Stereo Mi-croscope and X-ray Microtomography to StudyChanges in Wettability due to Microbial EnhancedOil Recovery at the Pore-scale

The effect of inherent wettability on recovery was studiedwithin 2D micromodels imaged with stereomicroscopy and3D columns imaged with x-ray microtomography. Water-wet to oil-wet surface ratios were produced in ratios: 1:5,5:5, and 5:1 by treating a fraction of the pore space withoctodecylthrichlorosilane, such that the spatial coordinatesof surface wettability are defined. Interfacial curvature, oilblob morphology, and additional oil recovered are reportedfor each mixed-wet system, prior to and after MEOR.

Dorthe Wildenschild, Ryan T. ArmstrongOregon State Universitydorthe@engr.orst.edu, armstror@onid.orst.edu

MS47

A Heterogeneous Multiscale Method (HMM) forTwo-phase Flow in Porous Media

We present a formulation of heterogeneous multiscalemethod (HMM) for two phase flow in porous media. Stan-dard macroscopic (Darcy’s Law) equations are augmentedwith a network flow model on pore (micro) scale. Networkflow model captures flow pathway details true to the porousmedium geometry. We exemplify macro-micro iteration fortwo-phase flow in 1D and 2D, as well as using a conceptualmodel of hydraulic fracture propagation.

Chia-Chieh ChuUniversity of Texas at Austinccchu@math.utexas.edu

Bjorn EngquistUT Austinengquist@math.utexas.edu

Masa ProdanovicUniversity of Texas at AustinDepartment of Petroleum and Geosystems Engineeringmasha@ices.utexas.edu

Yen-Hsi R. TsaiUniversity of Texas at Austin, USAytsai@math.utexas.edu

MS47

Thermodynamic Equi-

106 GS11 Abstracts

librium In Multiphase Porous Media: ExaminingEquilibria Across Spatial Scales

Macroscopic formulations for multiphase flow in porousmedia rely on thermodynamics to provide a closure re-lationship for the capillary pressure. Obtaining a validmacroscopic formulation is contingent on specification ofmacroscopic thermodynamics that are defined in a waythat is consistent with microscopic thermodynamics. Thistalk will address the challenges associated with developinga macroscopic definition for capillary pressure by consid-ering equilibration of multiphase systems over a range ofspatial scales and their relationship to more general mul-tiphase flow processes. Simulations performed using thelattice Boltzmann method will be used to illustrate the dif-ficulties associated with macroscopic averages of capillarypressure and to suggest an appropriate course of action.

James E. McClureDepartment of Environmental Sciences and EngineeringUniversity of North Carolina at Chapel Hilljemcclur@email.unc.edu

Casey MillerUniversity of North Carolinacasey miller@unc.edu

William G. GrayUniversity of North Carolina - Chapel Hillgraywg@unc.edu

MS47

Dynamic Capillary Effects in Unsaturated FlowThrough Deformable Porous Media

In recent years, non-equilibrium capillary effects in multi-phase flow in porous media have been investigated by manyauthors based on experimental work or numerical simula-tions. However, all the previous work has been done for theflow in rigid porous media. In this work, we investigate thedynamic capillary effects in deformable porous media usingnumerical modeling. We consider 1D consolidation modelincorporating the dynamic capillary pressure term, and weillustrate and discuss the numerical results.

Son-Young YiThe University of Texas at El Pasosyi@utep.edu

MS48

Stochastic Modeling of Complex Multi-phase Flowsto Link Pore and Darcy Scale Dynamics

To simulate complex non-equilibrium multi-phase flow inporous media a Lagrangian modeling framework was de-vised, which employes computational particles as statisticalrepresentatives of individual fluid elements. This approachallows to describe certain phenomena in a completely newand more natural way. The main advantage, however, isits ability to represent complex joint distributions and toaccount for effects of unresolved features, e.g. the evolu-tion of gravity fingers can be described without resolvingthem.

Patrick JennyInstitute of Fluid DynamicsETH-Zentrumjenny@ifd.mavt.ethz.ch

Manav TyagiETH ZurichInstitute for Fluid Dynamicstyagi@ifd.mavt.ethz.ch

MS48

Numerical Upscaling of Flows in Highly Heteroge-neous Porous Media

The generalized Stokes equations (called also Brinkmanequations),

−μΔu + ∇p + μκ−1u = f, ∇ · u = 0 inΩ,

where μ is the viscosity and κ is the permeability, are usedfor modeling flows in highly porous media. Motivated byindustrial applications of such materials we have developeda numerical method for comupting flows in heterogeneoushighly porous media with complicated internal structure ofthe permeability. We will present a two-scale finite elementapproximation of Brinkman equations. The method usestwo main ingredients: (I) discontinuous Galerkin finite el-ement method for Stokes equations, proposed and studiedby J. Wang and X. Ye (2007, SINUM, v. 45) and (II) sub-grid approximation developed by T. Arbogast for Darcyequations (2004, SINUM, v. 42). A number of numericalexamples will be presented to demonstrate the performanceof the subgrid method and an iterative method based it.

Raytcho Lazarov

Math Department/Inst. for scientific ComputattionTexas A&M Universitylazarov@math.tamu.edu

Joerg WillemsRICAM and the University of Linzjoerg.willems@gmail.com

MS48

Multilevel Multiscale Mimetic (M3) Method forSubsurface Transport Problems in HeterogeneousMedia

In our work we develop a multiscale method for modelingsubsurface contaminant transport within the framework es-tablished by the Multilevel Multiscale Mimetic method. Inthis method a multilevel hierarchy of coarse-scale systemsis constructed through a recursive coarsening procedure.The procedure involves an exact and approximate step andis locally conservative at all levels. Mimetic Finite Differ-ence (MFD) method is a basis of this hierarchy. The pres-ence of convection terms along with anisotropic diffusionterms introduce additional challenges for multiscale meth-ods. Possible solutions for different regimes and unsolvedissues will be presented in this talk.

Konstantin Lipnikov, Daniil SvyatskiyLos Alamos National Laboratorylipnikov@lanl.gov, dasvyat@lanl.gov

David MoultonLos Alamos National LaboratoryApplied Mathematics and Plasma Physicsmoulton@lanl.gov

MS48

Mortar Multiscale Methods for Stokes-Darcy

GS11 Abstracts 107

Flows in Irregular Domains

We study multiscale numerical approximations for the cou-pled Stokes-Darcy flow system. The equations in the coarseDarcy elements (or subdomains) are discretized on a finegrid scale by a multipoint flux mixed finite element methodthat reduces to cell-centered finite differences on irregulargrids. The Stokes subdomains can be discretized by anystable Stokes elements, including discontinuous Galerkin.The subdomain grids do not have to match across the inter-faces. Continuity conditions between coarse elements areimposed via a mortar finite element space on a coarse gridscale. With an appropriate choice of polynomial degree ofthe mortar space, we derive optimal order convergence onthe fine scale for the multiscale pressure and velocity. Thealgebraic system is reduced via a non-overlapping domaindecomposition to a coarse scale mortar interface problemthat is solved using a multiscale flux basis. Numerical ex-periments are presented to confirm the theory and illus-trate the efficiency and flexibility of the method.

Ivan YotovUniveristy of PittsburghDepartment of Mathematicsyotov@math.pitt.edu

Danail VassilevUniversity of Pittsburghdhv1@pitt.edu

MS49

Building a Reproducible Research Community:Experience of the Madagascar Open-source Project

Madagascar (http://www.ahay.org) is an open-softwareproject, which has been in existence for nearly 5 years andhas accumulated nearly 100 reproducible research publica-tions, mostly in applied geophysics and reflection seismol-ogy. Madagascar is released under the GPL license anddeveloped by a community of two dozen developers spreadaround the world between industry and academia. I willdescribe the main design principles and the experience ofimplementing and maintaining a reproducible research dis-cipline, which implies integrating computational results, in-cluding input data and open software code, with scientificpublications. Reproducible research enables higher levelsof scientific scrutiny and collaboration but requires a com-munity support to provide a continuous maintenance ofreproducible results.

Sergey FomelUniversity of Texas at Austinsergey.fomel@beg.utexas.edu

MS49

The GeoClaw Software for Depth-averaged Flowswith Adaptive Refinement

Many geophysical flow or wave propagation problems canbe modeled with two-dimensional depth-averaged equa-tions, such as shallow water equations. The GeoClaw soft-ware (www.clawpack.org/geoclaw) has been designed tosolve problems of this nature, using high-resolution shock-capturing finite volume methods and handling flow on to-pography and dry states, and incorporating AMR to allowthe efficient solution of large-scale geophysical problems.This open source software consists of Fortran programs to-gether with Python tools for the user interface and flow

visualization.

Randall J. LeVequeApplied MathematicsUniversity of Washington (Seattle)rjl@uw.edu; rjl@amath.washington.edu; rjl@washingt

Marsha BergerCourant Institute of Mathematical SciencesNew York Universityberger@cims.nyu.edu

David L. GeorgeDepartment of Applied MathematicsUniversity of Washingtondgeorge@amath.washington.edu

Kyle T. MandliUniversity of WashingtonDept. of Applied Mathematicsmandli@amath.washington.edu

MS49

DOLFWAVE: a FEniCS Application for WaterWaves Simulation

In this talk, we present DOLFWAVE, i.e., an applica-tion for solving surface water waves problems. A classof improved fourth-order Boussinesq-type models to simu-late the propagation and generation of dispersive wavesis derived. To approximate their solutions a continu-ous/discontinuous Galerkin finite element method with in-ner penalty terms is proposed. Dissipative effects and wavegeneration due to a time dependent varying sea bed are in-cluded. To demonstrate the applicability of the numericalscheme, several test cases are considered.

Nuno LopesCentro de Matematica e Aplicaoes Fundamentais, Lisboandl@ptmat.fc.ul.pt

Pedro PereiraInstituto Superior de Engenharia de Lisboappereira@deq.isel.ipl.pt

L. TrabuchoFaculdade de Ciencias e Tecnologia,Universidade Nova de Lisboatrabucho@ptmat.fc.ul.pt

MS49

The Central Role of Geophysics in the Repro-ducible Research Movement

I will trace the history of reproducible research in geo-physics and its subsequent influence in other fields, suchas computational harmonic analysis. A comparison of thisapproach to other forms of scientific communication sug-gests an urgent need to restructure the current scientificpublication process to encompass the reproducible researchprinciples pioneered in geophysics.

Victoria StoddenColumbia UniversityStatisticsvcs@stanford.edu

108 GS11 Abstracts

MS50

Multi-GPU Tsunami Simulation on TSUBAMEGPU Supercomputer

One of the most destructive natural disasters on Earthis a Tsunami hence the importance of an accurate andearly warning. A large-scale ocean-wide Tsunami simula-tion is presented utilizing the next-generation technologyGPGPU to push the envelop speeding up our computingfor single and multi-GPU on desktops and Tsubame SuperComputer. A highly accurate and conservative numericalscheme was used with a mesh adaptation for benchmarktests and a real case scenario

Marlon R. Arce AcunaGlobal Scientific Information and Computing centerTokyo Institute of Technologymarlon.arce@sim.gsic.titech.ac.jp

MS50

Efficient Shallow Water Simulations on GPUs

In this talk, we introduce the shallow water equations andtheir importance in geosciences, giving an overview of ap-plication areas and simulation approaches. The main focusis on physical phenomena; including flooding, dam breaks,tsunamis, and storm surges; and we discuss how simula-tions can be mapped to execution on GPUs. We furtheraddress precision aspects through validation and verifica-tion, and show that fast single precision calculations canbe sufficient to capture real-world flows.

Andr’e R. BrodtkorbSINTEF ICT, Department of Applied MathematicsAndre.Brodtkorb@sintef.no

MS50

Complex Shallow Water Simulations ThroughLattice-Boltzmann-Based Mesoscopic NumericalTreatment Exploiting Hybrid Compute Nodes

The talk presents stable and efficient fluid dynamics solversbased on Lattice-Boltzmann Methods (LBM) for ShallowWater type models. The mesoscopic nature of the LBM isexploited by modifying its boundary treatment and propa-gation/collision operators and adapting them to the spec-ified scenario on the particle and/or macroscopic level.With a slight focus on GPUs, the hardware-oriented de-sign and parallelisation on all levels is addressed – fromvectorisation via the multi-core-level up to full (hybrid)clusters.

Markus GevelerInstitute for Applied mathematics, TU DortmundUniversityGermanymarkus.geveler@math.tu-dortmund.de

MS50

Improving PVM finite volume schemes usingGPUs. Application to shallow flows

In this work, we extend the PVM finite volume numericalschemes introduced recently by Castro and Fernandez fornon-conservative hyperbolic systems to non-structured tri-angular meshes. An efficient GPU implementation usingthe Compute Unified Device Architecture (CUDA) frame-work has been performed, and applications to two-layershallow water systems are carried out. The numerical tests

show the benefits of the CUDA implementation with re-spect to an OpenMP CPU implementation.

Marc de la AsuncionDpto. Lenguajes y Sistemas Inform’aticos, ETSIITUniversidad de Granadamarc@correo.ugr.es

MS51

Moist Thermodynamics in Sound-proof Simulation

This presentation will discuss moist simulation applyingatmospheric sound-proof equations. The key issue is thatthe phase changes in moist thermodynamics are affectedby the temperature and pressure perturbations. In thesound-proof system, however, pressure perturbations arenot readily available and only the hydrostatically-balancedenvironmental pressure profile is used in the moist ther-modynamics. Accuracy of such an approach will be dis-cussed and illustrated with simple numerical experimentswith sound-proof and fully-compressible systems of equa-tions.

Wojciech GrabowskiNCAR’grabow@ucar.edu’

MS51

On the Asymptotic Range of Validity of Sound-proof Atmospheric Flow Models

Several versions of sound-proof model equations for atmo-spheric flows have been suggested in the past. Ogura andPhillips (1962) assumed a stratification of potential tem-perature of the order of the Mach numer, M , squared,which results in the characteristic times of advection andinternal gravity waves to be of the same order in M. Thisallowed them to adopt classical single-scale asymptotics toeliminate the sound modes and to arrive at their anelas-tic model equations. However, with M 0.03, one hasM2 1.0e − 3. Potential temperature variations across thepressure scale height would be restricted to less than 1 Kin this regime which is in contrast with realistic values of30–50 K. In this lecture I will summarize recent effortsat systematically justifying sound-proof models for muchstronger stratifications in realistic three time scale asymp-totic regimes.

Rupert KleinFreie Universitat Berlinrupert.klein@math.fu-berlin.de

MS51

Baroclinic Instability in Sound-Proof Global Sim-ulations

We use an anelastic model, EULAG, to simulate thegrowth, propagation, and breaking of planetary wavesin the baroclinic instability test of Jablonowski andWilliamson. Solutions yield very similar growth rates, dis-turbance amplitudes, and phase speeds during the lineargrowth regime. After ∼ 8 days, wavebreaking commences,at which point EULAG results begin to depart in some de-tails from those of JW. Nevertheless, general agreement inthe global structure of the solution remains.

Joseph M. PrusaTeraflux Corporation

GS11 Abstracts 109

jprusa@bellsouth.net

William GutowskiIowa State Universitygutowski@iastate.edu

MS51

Sound-proof Simulations of Atmospheric WavePhenomena

We investigate the performance of several sound-proofmodels, including the anelastic Lipps-Hemler and thepseudo-incompressible Durran nonhydrostatic equations.Physics wise, our primary interests are with the dynamicsof inertia-gravity waves, an important element of weatherand climate. Our numerical developments are based ona class of nonoscillatory forward-in-time methods and areapplicable to global and limited area models. Challeng-ing simulations of atmospheric wave phenomena involvestructured-grid and unstructured-mesh discretizations.

Piotr SmolarkiewiczNCARMMMsmolar@ucar.edu

Joanna SzmelterLoughborough Universityj.szmelter@lboro.ac.uk

MS52

Rupture Arresting due to 3D Effects in LargeEarthquakes

Large events are originated in large aspect-ratio faults inwhich the fault length (L) is very larger than fault width(W). Previous studies (Day, 1982) shows that this kindof fault initially ruptures as a crack-like, but subsequentlythe rupture bifurcates into two separate pulses travelingin opposite directions. When this process occurs in thebi-material case (Dalguer and Day, 2009), it evolves inter-acting with the normal stress perturbation (characteristicsof bimaterial fault rupture) and under very limited condi-tions it can lead to unilateral rupture, in which rupture isarrested in the non-preferred direction and rupture propa-gates indefinitely in the preferred direction. Here we con-tinue the investigation in this direction to further under-stand the W effect on rupture propagation. Our numericalinvestigation in homogeneous fault shows that W takes animportant role on rupture arresting and the generation ofsteady-state pulse-like rupture in strike slip as well as dip-ping faults due to the arrival of the stopping phases at therupture front. Rupture velocity depends on W. This de-pendence leads to slowdown the rupture speed, capable toarrest the rupture for small Ws. For W/Lc less than 4 and5.3, respectively for strike and dipping faults, rupture isarrested, in which Lc is the critical length. At large dis-tance, the rupture propagates with a steady-state velocitypulse. In a bimaterial fault, for the same problems, rup-ture never stops. These results suggest that the bimaterialeffects promote rupture and W effects promote rupture ar-resting. When combining W and bimaterial effects, bothare competing, and only under some limited conditions uni-lateral rupture originates. In these cases, the W effectssuccessfully arrest the rupture in the non-preferred direc-tion, while in the preferred direction the bimaterial effectenhance rupture propagation. Such as effect can also besignificant on tsunami generation, a topic currently under

research.

Luis DalguerSwiss Seismological Service, ETH ZurichSonneggstrasse 5, CH-8092 Zurich, Switzerlanddalguer@sed.ethz.ch

Jean P. AmpueroCalifornia Institute of TechnologySeismological Laboratoryampuero@gps.caltech.edu

MS52

Tsunami Simulation and Earthquake Source Iden-tification using GeoClaw

GeoClaw (www.clawpack.org/geoclaw) is an open sourcesoftware package that solves the shallow water equationsmodeling tsunami propagation and inundation using adap-tive mesh refinement, allowing for rapid simulation oftsunamis from known sources. Recently we have experi-mented with tsunami source inversion using the GeoClawcode together with data from NOAA’s DART buoys, whichprovide real-time data on sea surface elevation as a tsunamipasses by. The goal is to rapidly estimate the seafloor de-formation that caused the tsunami in order to simulate thefurther propagation of the tsunami.

David GeorgeUSGS Cascades Volcano Observatorydave.jorge@gmail.com

Randall J. LeVequeApplied MathematicsUniversity of Washington (Seattle)rjl@uw.edu; rjl@amath.washington.edu; rjl@washingt

MS52

The Discontinuous Galerkin Method for ModelingDynamic Earthquake Rupture on Complex Faults

Modelling the dynamics of the earthquake rupture processis a key component for physics-based simulation of the slipdistribution. For undersea earthquakes the resulting oceanbottom displacement is crucial for tsunami generation. Wepresent the discontinuous Galerkin finite element methodfor modeling the behaviour of geometrically complicatedfaults in realistic subsurface conditions using unstructuredtetrahedral meshes. The approach is based on the numer-ical solution of the elasto-dynamic waves equation usingwell-established friction laws as internal boundary condi-tions at element interfaces aligned with the fault plane.

Martin Kaeser, Christian PeltiesLMU Muenchenkaeser@geophysik.uni-muenchen.de,pelties@geophysik.uni-muenchen.de

MS52

Earthquake Dynamics and Potential Tsunamis inthe Greater Antilles Subduction Zone

Using the 3D finite element method, we model the dynam-ics of potential earthquakes in the Greater Antilles Subduc-tion Zone, including the plate boundary thrust fault andthe strike-slip Septentronial and Bunce faults. We find thatearthquakes may propagate from the Septentronial fault tothe plate boundary thrust and vice versa; thus, there may

110 GS11 Abstracts

be more routes to a tsunamigenic earthquake than havebeen previously assumed in this region. We will discussimplications for tsunami generation.

David D. OglesbyDepartment of Earth Sciences, Univ. of CA, Riverside900 University Ave. Riverside, CA 92521david.oglesby@ucr.edu

Eric L. GeistUS Geological Surveyegeist@usgs.gov

Uri ten BrinkUS Geological SurveyWoods Hole, MAutenbrink@usgs.gov

MS53

Transient Non-isothermal Fully Coupled Well-bore/Reservoir Modeling

Abstract not available at time of publication.

Zhangxing ChenUniversity of Calgaryzhachen@ucalgary.ca

MS53

Enhanced Successive Substituion Algorithm forMultiphase Flash Calculations

Flash calculations are performed billions of times during acompositional flow simulation. The reliability of flash cal-culations greatly affects the robustness of the entire flowsimulation. Consequently, reducing its CPU time, as wellas improving its robustness enormously impacts compo-sitional flow modeling. Anderson Acceleration representsan efficient and elegant approach to enhance these calcu-lations. Anderson Acceleration is a general algorithm forenhancing convergence of fixed-point iterations. The ideaof Anderson acceleration is to take advantage the informa-tion obtained from multiple previous iterations to betterpredict the next iterate. We do not store all of the pre-vious iterates, nor we assign equal weights to all of them,since the early iterates may contain less predictive infor-mation. This acceleration approach has been applied towide ranges of problems, most notably in computations ofelectronic structure. When applied to linear problems, An-derson Acceleration is equivalent to the well-known GM-RES algorithm. We investigate the application of Ander-son Acceleration as a method to enhance phase behaviorflash calculations within the framework of reservoir com-positional modeling. In particular, we seek to improve theconvergence rate and convergence region of the commonSuccessive Substitution algorithm for oil-gas flash. We ob-tain results relating to the Simple Mixing algorithm, a spe-cial case of Anderson Acceleration, with improved perfor-mance of the Successive Substitution algorithm. We utilizebrute-force investigation to examine convergence behaviorfor various initial equilibrium ratios (K-values). We ob-serve that the convergence regions appear to widen out forcertain cases. We also compare this accelerated Succes-sive Substitution with plain Successive Substitution andNewton-type iterations, and we discuss its inclusion into aniterative-IMPEC finite-element multiphase computationalflow simulator.

Shuyu Sun

Division of Mathematical and Computer Sciences &EngineeringKing Abdullah University of Science and Technology(KAUST)shuyu.sun@kaust.edu.sa

Omar HinaiICESUniversity of Texas at Austinohinai@ices.utexas.edu

Mary F. WheelerCenter for Subsurface ModelingUniversity of Texas at Austinmfw@ices.utexas.edu

MS53

Local Velocity Postprocessing for Multipoint FluxMethods on General Hexahedra

In multiphase flow simulations, if one uses a finite volumemethod with a piecewise constant approximation for thesaturation/concentration equation, accurate face velocitiesare sufficient. For higher order methods such as discon-tinuous Galerkin method with piecewise linears, one needsaccurate velocity in the interior gridblocks. In this work, anefficient postprocessing technique is developed to get an ac-curate interior velocity based on an accurate face-velocityof the multipoint flux approximation method.

Mary F. WheelerCenter for Subsurface ModelingUniversity of Texas at Austinmfw@ices.utexas.edu

Guangri XueInstitute for Computational Engineering and SciencesUniversity of Texas at Austingxue@ices.utexas.edu

Ivan YotovUniveristy of PittsburghDepartment of Mathematicsyotov@math.pitt.edu

MS53

A Multiscale Stochastic Framework for CoupledSubsurface and Surface Flows

We discuss a multiscale stochastic framework for uncer-tainty quantification in modeling flow and transport insurface-subsurface hydrological systems. The governingflow equations are the Stokes-Darcy system with Beavers-Joseph-Saffman interface conditions. The permeability inthe Darcy region is stochastic and it is represented with aKarhunen-Loeve (KL) expansion. The porous media canbe statistically non-stationary, which is modeled by differ-ent KL expansions in different regions. Statistical momentsof the solution are computed via sparse grid stochastic col-location. The spatial domain is decomposed into a series ofsmall subdomains (coarse grid) of either Stokes or Darcytype. The flow solution is resolved locally (on each coarseelement) on a fine grid, allowing for non-matching gridsacross subdomain interfaces. Coarse scale mortar finiteelements are introduced on the interfaces to approximatethe normal stress and impose weakly continuity of flux.The transport equation is discretized via a local discon-tinuous Galerkin method. Computational experiments are

GS11 Abstracts 111

presented.

Ivan YotovUniveristy of PittsburghDepartment of Mathematicsyotov@math.pitt.edu

Benjamin GanisUniversity of Texas at AustinCenter for Subsurface Modelingbganis@ices.utexas.edu

Vivette GiraultUniversity of Paris VIgirault@ann.jussieu.fr

Danail Vassilev, Ming ZhongUniversity of Pittsburghdhv1@pitt.edu, miz17@pitt.edu

MS54

Thermodynamical Modelling of the Hydrogen Mi-gration in Argillite for a Deep Geological Radioac-tive Waste Repository - Numerical Validation

We introduce a compressible 2-phases 2-components modelof flow in porous media, with vaporisation and gas solu-bility, based on thermodynamical principles, and consis-tent with the any phase state: one single phase (liquidor gaseous) or two phases. Synthetic numerical simula-tions are presented for validation. They include the threemain problems which appeared in the ANDRA (Radioac-tive waste disposal French Agency) benchmark Couplex-Gas: phase appearance/disappearance - non equilibriumof the initial state - very high contrast in materials.

Alain P. BourgeatUniversite Lyon1UMR CNRS 5208bourgeat@univ-lyon1.fr

Magdalena DymitrowskaInstitut de Radioprotection et de Srete Nucleairemagdalena.dymitrowska@irsn.fr

Farid SmaiIRSN/DSU/SSIAD/BERISF -92262 Fontenay-aux-Roses cedex,Francefarid.smai@univ-lyon1.fr

MS54

3-Phase Stability in Methane Hydrates ThroughCapillary Inhibition and Pore Water Salinity

A common view of hydrate systems is that hydrate andwater are present in the stability zone, gas and water arepresent below, and gas, liquid and water coexist at theirinterface. However, we show that the three phase regioncan exist over a broad zone through two approaches: 1)gas flow and hydrate solidification elevates salinity; and 2)hydrate and free gas are present in pores of different sizedue to capillary effects.

Peter B. FlemingsThe University of Texas at AustinJackson School of Geosciencespflemings@jsg.utexas.edu

Xiaoli LiuExxonMobilxiaoli liu@yahoo.com

MS54

Phase Transitions in Coupled Models: Equilibriumand Kinetic Models

We consider phase change in multiphase multicomponentmodels in carbon sequestration, hydrate evolution, orblack-oil. The phase change from liquid to gas or hydrateresults from a constraint of maximum solubility of a com-ponent in the prevalent liquid phase. In computations,this can be realized in equilibrium. Alternatively, a kineticmodel guides the system through phase change on a localtime scale via an auxiliary ODE. We discuss advantagesand disadvantages of different approaches.

M PeszynskaOregon State Universitympesz@math.oregonstate.edu

MS54

Modelling Gas Transport in Coalbeds During Pri-mary and Enhanced Methane Recovery

As both a source and a reservoir rock, coalbeds can be char-acterised by two distinctive porosity systems: a networkof extensively-distributed natural fractures (termed cleats)and matrix blocks with a wide-range pore size distribution.Coal gas is mainly stored by adsorption, primarily in themicropores. During methane production, desorbed gas dif-fuses through matrix to enter cleats. This paper presentsnumerical approaches used for modelling gas transport incoalbeds during both primary and enhanced methane re-covery.

Ji-Quan Shi, Sevket DurucanImperial Collegej.q.shi@imperial.ac.uk, s.durucan@imperial.ac.uk

MS55

Numerical Simulation of Anomalous Transport inPorous Media Described by Fractional-advectionDispersion Equation

In the contribution, we present computational studies ofthe fractional-advection dispersion equation containing thefractional-derivative multidirectional diffusion term whichcan be responsible for anomalous transport effects. Knownjustification of this model relies on the relation with theLevy stochastic processes. The solution of the model ex-hibits anisotropic features and variety of interesting phe-nomena not observed in the Brownian diffusion. Numericalsolution of the transport equation leads to the linear sys-tems of equations with full matrices which slows down thesolution process. We couple the transport equation to thesingle-phase saturated flow in a heterogeneous medium andstudy the anomalous contaminant transport in it.

Michal BenesDepartment of MathematicsCzech Technical University in Praguebenesmic@kmlinux.fjfi.cvut.cz

Tissa H. IllangasekareCESEPColorado School of Mines

112 GS11 Abstracts

tissa@mines.edu

MS55

Application of Level Set Methods for GroundwaterFlow with Free Surface

Level set methods are popular numerical tools for descrip-tion and tracking of moving interfaces in many fields ofapplied mathematics. We present a level set formulationfor mathematical model of groundwater flow with free wa-ter table that separates the saturated zone from unsatu-rated one in porous media. The advantage of our levelset formulation is the possibility to use static (enlarged)computational domain with fixed computational grid forthe flow equation. The zero pressure boundary conditionsdefined on the water table are resolved numerically by ap-plications of immersed interface method in the frameworkof finite volume discretization. The movement of ground-water table and the extrapolation of physical quantitiesknown only on the water table are given by numerical so-lution of related advection equations. Several numericalexperiments will be presented that confirm the accuracyand the robustness of our level set methods.

Peter FrolkovicDepartment of MathematicsSlovak University of Technologypeter.frolkovic@stuba.sk

MS55

Compact and Stable Discontinuous Galerkin Meth-ods forConvection-Diffusion Problems

We present a new method, the Compact Discontinu-ous Galerkin 2 (CDG2) method, for solving nonlinearconvection-diffusion problems. Theoretical results showingstability of CDG2 for the heat equation are given, provid-ing explicit bound on any free parameters in the scheme.We present numerical tests for different problems, such asscalar advection-diffusion equations, two-phase flow , andfor compressible Navier-Stokes. We compare SIPG, BR2,CDG, CDG2, and LDG in terms of L2-accuracy and CPUtime.

Robert KloefkornUniversity of Freiburgrobertk@mathematik.uni-freiburg.de

Andreas DednerUniversity of Warwicka.s.dedner@warwick.ac.uk

Slavko BrdarUniversity of Freiburgslavko@mathematik.uni-freiburg.de

MS55

A New Inflow-Implicit/Outflow-Explicit FiniteVolume Method for Solving Variable Velocity Ad-vection Equations

We discuss a new method for solving non-stationary advec-tion equations. The method is based on finite volume spacediscretization and a semi-implicit discretization in time. Itsbasic idea is that outflow from a cell is treated explicitlywhile inflow is treated implicitly. The method is exact forconstant velocity transport of quadratic functions for any

length of a time step and it is second order accurate forsmooth solutions in general. The matrix of the system isdetermined by the inflow fluxes which results in a M-matrixyielding favourable stability properties for the scheme. Themethod allows large time steps at a fixed spatial grid with-out losing stability and not deteriorating precision. Thismakes it attractive for practical applications. The schemeis well suited for variable velocity vector fields in higherdimensions and for nonlinear advection-diffusion problemswhich is documented by a series of numerical experiments.

Karol MikulaDepartment of MathematicsSlovak University of Technologykarol.mikula@gmail.com

Mario OhlbergerUniversitat MunsterInstitut fur Numerische und Angewandte Mathematikmario.ohlberger@uni-muenster.de

MS56

Numerical Homogenization for Complex Multi-phase Porous Media Flow

We present a multiscale approach for multiphase porousmedia flow based on numerical homogenization. The mul-tiscale method consists of a pore scale phase-field multi-phase flow solver coupled to a macroscopic finite volumesolver. The coupling between the solvers is done through amacroscopic pressure gradient which enters the pore-scalesimulations and averaged microscopic fluxes which are usedin the finite volume solver. The method is able to handlearbitrary number of flow phases and allows to include non-linear effects such as contact angles and surface tensionin a straightforward way. For single phase and simplifiedtwo-phase flow problems the approach is consistent withexisting homogenization results.

Lubomir BanasDepartment of MathematicsHeriot-Watt Universityl.banas@hw.ac.uk

MS56

CTRW-based Methodology for Studying the Im-pact of Heterogeneities on Transport at MultipleScales

The advantages offered by a methodology that unifies porenetwork modeling, CTRW theory and experiment in up-scaling solute transport in porous media are presented.Temporal probability density functions of tracer particlesexplain the physical origin of the power-law scaling of dis-persion coefficient vs. Peclet number. The rich Peclet-number dependence of asymptotic dispersion coefficient ispredicted from first principles and compares well with ex-perimental data for restricted diffusion, transition, power-law and mechanical dispersion regimes. However, until thevelocity field is fully sampled, transport is non-Gaussian.This opens up the question on the nature of dispersion innatural systems where the heterogeneities at larger scalessignificantly increase the range of velocities in the reser-voir, thus delaying approach to Gaussian behaviour. Todescribe it, the multi-scale approach is used in which trans-port at core, gridblock and field scale is viewed as a seriesof particle transitions between discrete nodes governed byprobability distributions. At each scale of interest a distri-bution that represents transport physics (and heterogene-

GS11 Abstracts 113

ity) is used as an input to model a subsequent reservoirscale. Statistically rare events such as an encounter witha low velocity zone, have an especially large effect on theplume transport. The cause of anomalous behavior is thebroad spectrum of rates or transition times engendered bythe heterogeneities.

Branko BijeljicDepartment of Earth Science and EngineeringImperial College Londonb.bijeljic@imperial.ac.uk

Martin BluntDept. Earth Science and EngineeringImperial College Londonm.blunt@imperial.ac.uk

Matthew RhodesChevron North Sea LtdChevron Energy Technology Companymatt.rhodes@chevron.com

MS56

Unstable Displacements in Multiphase Flow inPorous Media: Continuum Modeling and Simula-tion Challenges

Continuum modeling of wetting phenomena is importantin many scientific and engineering applications, from mi-crofluidics and multiphase flow to flow and transport inpermeable media. Here we discuss the development ofphase-field models of multiphase flow, with particular em-phasis on viscous-unstable displacements. The proposedmodel is used to simulate the transport of a passive scalarthrough one of the fluids. We show that viscous fingeringinstabilities enhance mixing at low Reynolds numbers, anddiscuss the discretization techniques used in our simula-tions.

Luis Cueto-Felgueroso, Ruben JuanesMITCivil and Environmental Engineeringlcueto@mit.edu, juanes@mit.edu

MS56

Analysis and Parameterization of Continuum-ScaleTheories using Pore-Network Models- Applicationfor Non-equilibrium Capillarity Theories

Among different numerical and experimental methodsfor investigation of flow and transport in porous me-dia, pore-scale simulators are of great importance dueto their detailed physical-based structure compared tothe continuum-scale models as well as their inexpen-sive tractability compared to the laboratorial methods.Although there are different pore-scale simulators suchas Lattice Boltzmann, smoothed particle hydrodynamics,level set, etc., pore-network models are still the mostextensively-used approach due to their rather inexpensivecomputational cost that allows simulating larger domains.We have employed dynamic pore-network modelling toanalyse the non-equilibrium capillarity effects in porousmedia and parameterize the phenomena for continuum-scale models. This study is fulfilled in three steps: a) Pore-scale simulation of two-phase flow: using a dynamic pore-network simulator, DYPOSIT, two-phase drainage processin a conceptual porous medium is simulated under Dirich-let boundary conditions. b) Averaging the pore-scale infor-mation to obtain the Darcy-scale entities: after fulfillment

of the simulations, the local information are averaged us-ing moving window averaging to obtain the Darcy-scaleentities, required for analysis of the Darcy-scale formula-tions. c) Defining the Darcy-scale parameters: this post-processing step involves determination of the parametersintroduced in extended two-phase flow equations using thedata obtained in the previous step. The relations derivedin this step can be incorporated in continuum-scale simu-lators for two-phase flow in porous media to model largescale domains.

Vahid Joekar-NiasarDepartment of Earth SciencesUniversity of Utrechtjoekar@geo.uu.nl

S. Majid HassanizadehUtrecht Universityhassanizadeh@geo.uu.nl

MS57

Mixed Multiscale Finite Element Methods forTwo-phase Flow in High-contrast Porous Media

The simulation of fluid flow in fractured rock is challengingdue to the high contrast in the permeability. We present amixed multiscale finite element method with a coarse-scaleapproximation space which captures fine-scale effects offlows in such high-contrast applications. The coarse spaceis related to a domain decomposition method designed forpreconditioning the fine-scale problem. We demonstratethe effectiveness of our approach with numerical examplesand discuss the use of these coarse spaces in precondition-ing of mixed finite element methods.

Dylan CopelandTexas A&M Universitydylancopeland@gmail.com

Yalchin EfendievDept of MathematicsTexas A&M Universityefendiev@math.tamu.edu

MS57

A Multiscale Preconditioner for Nonlinear Multi-physics Problems in Porous Media

The mortar mixed finite element method can be viewedas a multiscale method, with recent developments showingthat the construction of a multiscale flux basis can greatlyreduce the computational cost for the domain decompo-sition problem. Computing this multiscale basis can beexpensive, but we show that the basis does not need to berecomputed for each time step if used as a preconditioner.This approach can also be extended to nonlinear interfaceproblems and we provide numerical results illustrating theefficiency of this technique on fully implicit formulationsfor multiphase flow.

Gergina Pencheva, Ben GanisUniversity of Texas at Austingergina@ices.utexas.edu, bganis@ices.utexas.edu

Tim M. WildeyThe University of Texas at AustinAustin, USAtwildey@ices.utexas.edu

114 GS11 Abstracts

Mary F. WheelerCenter for Subsurface ModelingUniversity of Texas at Austinmfw@ices.utexas.edu

Ivan YotovUniveristy of PittsburghDepartment of Mathematicsyotov@math.pitt.edu

MS57

Two-Stage Algebraic Multiscale Linear Solver forFlow in Highly Heterogeneous Formations

We address two aspects that pose a serious challengeto existing multiscale finite-volume formulations, namely,channel-like features and strongly anisotropic transmissi-bility. We describe a Two-stage Algebraic Multiscale Solver(TAMS) for the pressure linear system. One stage dealswith a global coarse-grid problem and the second stage usesa local preconditioner on the fine-grid. TAMS converges tothe fine-grid solution efficiently in those challenging casesand guarantees conservation after every iteration.

Hamdi TchelepiPetroleum Engineering DepartmentStanford Universitytchelepi@stanford.edu

Hui ZhouStanford Univ.huizhou@stanford.edu

MS58

On The Tyranny Of Corner Point Grids

The corner point grid is ubiquitous in the petroleum in-dustry. It is used to represent reservoir structure andfaults, reservoir stratigraphy and layering, and static anddynamic properties on the grid. A corner point grid hasthree main characteristics: geometry, topology, and trans-formed transport properties. Of these three characteristics,we will provide examples of the limitations of each, and de-scribe how the topology of the grid is typically the mostrestrictive aspect of the description.

Michael J. KingTexas A&M Universitymike.king@tamu.edu

MS58

Simple Grid Generation Algorithms for FracturedPorous Media

This talk describes grid generation algorithms for fracturedporous media. Unlike gridding techniques designed for in-put geometry that is known precisely, our approach forfractures is designed to only capture details of the fracturenetwork geometry larger than the specified grid resolution.The final grids honor fractures approximately while main-taining good cell quality. Several numerical examples arepresented in two and three dimensions that demonstratethat the algorithms are robust and practical for industrialapplications.

Brad MallisonChevron Energy Tech. Co.btmb@chevron.com

MS58

Unstructured Hybrid Element Meshing for Reser-voir Simulation

Although popular in civil engineering, fully unstructuredfinite-element meshing is rarely used in reservoir simula-tion. Critics argue that it is too complicated to apply togeologic structures. Here, we show that it is feasible andhas many advantages over structured gridding. We presenta workflow including indirect meshing strategies for largeaspect ratio features like faults and fractures. When thisdiscretization is permitted by the physics of interest we alsouse lower dimensional finite-element representations.

Stephan K. MatthaiMontan University of LeobenLeoben, Austriastephan.matthai@gmail.com

Julian MindelMontan University of Leoben, Austriajulian.mindel@unileoben.ac.at

MS58

On Reservoir Gridding for Assessment of Struc-tural Uncertainty

Structural uncertainty refers to uncertainties of the struc-tural framework; i.e. position, orientation, shape and trun-cations of geological faults and horizons. Structural un-certainty is in general a major uncertainty in the sub-surface description, but has been cumbersome to assessexplicitly. We will discuss and exemplify limitations of theindustry standard for 3D gridding with respect to geomet-ric representation the structural framework. Moreover, wewill present methodology for parametric updating of thestructural-framework representation in 3D grids.

Vegard R. Stenerud, Oddvar LiaStatoil ASAvrst@statoil.com, olia@statoil.com

MS59

Computational Infrastructure for Geodynamics

Scientific computation has long played a key role in solidEarth geosciences; quantitative numerical models providea critical link between observations at Earth’s surface anddynamic processes in the interior. With increases in com-putational power and sophistication of algorithms, solidEarth geoscience has seen a proliferation of powerful andpredictive models for these problems. Targets for devel-opment include models that leverage algorithmic advancesto enable exploration of the fundamental interactions be-tween the different Earth systems. Such coupled, inter-disciplinary problems are becoming a target of research insolid Earth geodynamics. Examples include the interac-tion of the lithosphere, plate boundaries and the deepermantle, the role of fluids in lithospheric deformation, thebehavior of faults in the crust, and long-term thermal evo-lution of the planet. To improve our understanding of theseproblems using scientific computation, the ComputationalInfrastructure for Geodynamics (CIG) was established asa community partnership between geophysics and compu-tational science. CIG provides advanced computationaltools to the geoscience community, to enable geoscientiststo more effectively explore and understand the dynamics ofour planet. This talk will discuss mathematical and com-putational issues and directions for development in com-

GS11 Abstracts 115

putational geodynamics at CIG.

Louise KelloggDepartment of GeologyUniversity of California Daviskellogg@ucdavis.edu

MS59

Thermomechanics of Mid-ocean Ridge Segmenta-tion

Abstract not available at time of publication.

Luc LavierInstitute For GeophysicsUniversity of Texas Austinluc@utig.ig.utexas.edu

MS59

Generation and Extraction of Magma: A Multi-scale, Multiphysics Geodynamics Problem

Upscaling algorithms and robust multiphysics solvers arekey to model the generation and extraction of melt. Heatand chemical exchange are present from grain to platescale. Self-organization produces channels but their inter-action with large-scale structures and their time evolutionare yet unknown. Can they result in magma chambers?Viscosity contrasts of 1020 are present. Dike intrusionsoccurs at much shorter time scale than mantle flow yetrepresent the final stage of melt delivery.

Laurent MontesiDepartment of GeologyUniversity of Marylandmontesi@umd.edu

MS59

Emerging Geodynamic Computational Techniquesat the Victoria Partnership for Advanced Comput-ing

I will survey the parallel implementation of the particle-in-cell finite element code, Underworld, and explain how themethodology was designed to attack specific geodynam-ics problems. I will give an overview of the relationshipbetween this method and other particle-based approachesand show discuss the relative merits of this method (includ-ing its disadvantages). By tracking representative materialpoints, the method is able to take account of the strong,history-dependent material non-linearities and fabric de-velopment which emerge during large-scale deformationand accompanying localisation. Underlying the methodis a standard finite element engine which relies on a ro-bust, implicit multigrid-method to solve the stress-balanceequations for incompressible, Stokes’ flow. The methodallows for the tracking of sharp material interfaces, dis-continuities and strong localisation which, in turn, createsvery large variations in material properties. Careful tun-ing of the solvers is required to develop efficient, scalableparallel solvers that can also cope with these variations ina robust manner. Application areas for Underworld typi-cally range from the crustal scale deformation and evolu-tion of basins, studies of subduction zone dynamics andorogeny, to regional mantle convection simulations withmany tens to hundreds of thousands of time-steps. Themethod is also useful for transferring geological structuralmodels into thermal-mechanical models since it is not nec-essary to mesh all interfaces and structures exactly in order

to consider their influence on the system.

Louis MoresiSchool of Mathematical SciencesMonash Universitylouis.moresi@monash.edu

MS60

Optimization Techniques for Triangular AdaptiveMesh Refinement

The simulation of many geophysical problems comprises alarge range of spatial and temporal scales. In computingthe effect of mixing on cloud evolution, the typical cloudcluster length scale tens of kilometers, while accurate mix-ing is modeled with spatial resolution of approx. a meter.In order to numerically bridge this span of scales, adaptivemesh refinement (AMR) methods play an important role.This presentation introduces recent advances in optimizingthese methods.

Joern BehrensKlimaCampus, University of Hamburgjoern.behrens@zmaw.de

Oliver KunstKlimaCampusUniversity of Hamburgoliver.kunst@zmaw.de

MS60

A High-order Adaptive Global Shallow WaterModel

Unstructured meshes are becoming more and more popularin geophysical flow models. We present a two-dimensionalmodel solving the shallow water equations on unstructuredmeshes. The latter is dynamically adapted using the AMRtechnique to minimize the discretization error. The inter-polation order is also adapted during the solution process.Classical test cases on the sphere are used to validate themodel, as well as the global simulation of the 2010 tsunamiin Chile.

Sebastien BlaiseNational Center for Atmospheric Researchsblaise@ucar.edu

MS60

An Adaptive Discontinuous Galerkin Method forModeling the Compressible, 2D Navier-StokesEquations

Theoretical understanding and numerical modeling of at-mospheric moist convection still pose great challenges tometeorological research. The present work addresses thefollowing question: How important is mixing betweencloudy and environmental air for the development of acumulus cloud? A Direct Numerical Simulation of a sin-gle cloud is way beyond the capacity of today’s comput-ing power. The use of a Large Eddy Simulation in com-bination with semi-implicit time-integration and adaptivetechniques offers a significant reduction of complexity. Sofar this work is restricted to two-dimensional geometry.The compressible Navier-Stokes equations are discretizedusing a discontinuous Galerkin method introduced by Gi-raldo and Warburton in 2008. Time integration is doneby a semi-implicit backward difference from Restelli and

116 GS11 Abstracts

Giraldo (2008). For the first time we combine these nu-merical methods with an h-adaptive grid refinement. Thisrefinement of our triangular grid is implemented with thefunction library AMATOS and uses a space filling curve ap-proach (Behrens, 2005). Validation through different testcases shows very good agreement between the current re-sults and those from the literature. For comparing differ-ent adaptivity setups we developed a new qualitative errormeasure for the simulation of warm air bubbles. With thehelp of this criterion we show that the simulation of a risingwarm air bubble on a locally refined grid can be four timesfaster than a similar computation on a uniform mesh withthe same accuracy.

Andreas MullerInstitute for Atmospheric PhysicsMainz Universityandrmue@uni-mainz.de

Jorn BehrensKlimaCampusUniversity Hamburgjoern.behrens@zmaw.de

Francis X. GiraldoNaval Postgraduate Schoolfxgirald@nps.edu

Volkmar WirthInstitute for Atmospheric PhysicsMainz Universityvwirth@uni-mainz.de

MS60

A h-p Adaptive Simulation Environment for Atmo-spheric Sciences

We present a framework aimed at problems arising in thegeosciences: it can solve the non-hydrostatic equations ofthe atmosphere, shallow-water problems, tsunami predic-tion and advection tests. The DG method is employed,however, any element based discretization can be sup-ported. A mesh database enables parallel non-conformingmesh refinements in both h-p. Modern coding techniquesare employed. The latter permit the seamless optimizationof compute kernels: SSE vector type are now supportedbut could be extended to GPUs.

Amik St CyrInstitute for Mathematics Applied to Geosciences ,NCAR , 1850 Table Mesa Drive, Boulder CO 80305, USA.amik@ucar.edu

Sebastien BlaiseNational Center for Atmospheric Researchsblaise@ucar.edu

David HallNational Center for Atmospheric Research1850 Table Mesa Drive, Boulder CO 80305halld@ucar.edu

MS61

The Butterfly Algorithm for Radar Imaging andWave Propagation

The butterfly algorithm is a robust alternative to the FFTfor computing oscillatory integrals in a fast and accurate

manner. At the core of the algorithm, low-rank interac-tions are updated in a hierarchical fashion up and downquadtrees. We review the method, its expected accuracy,and applications to synthetic aperture radar imaging andwave propagation for geophysical applications. Joint workwith Matt Ferrara, Nick Maxwell, and Lexing Ying.

Laurent DemanetMathematics, MITdemanet@gmail.com

MS61

Homogenization of Wave Equations with Non-separated Scales

We consider the numerical homogenization of acousticwave equations (and elastodynamics equations) with het-erogeneous coefficients, namely, when the bulk modulus(elasticity tensor) and the density of the medium are onlybounded. We show that if source terms, boundary condi-tions and initial conditions are (integrable) regular enoughthen, eigenvectors associated with large frequencies areonly weakly excited, and it is possible to homogenize theoriginal problem. This homogenization is made possible,not by ergodicity assumptions, but by the observation that,if the source terms are in the unit ball of L2 (instead ofH−1), then the solution space is compact in H1, withrespect to the H1-norm. Various parts of this talk arejoint work with L. Zhang, L. Berlyand, M. Desbrun, L.Kharevych and P. Mullen.

Houman OwhadiApplied MathematicsCaltechowhadi@caltech.edu

MS61

Upscaling Finite Element Methods for Wave Prop-agation

Materials such as rock and disordered composites tend toexhibit heterogeneity at many (ideally, a continuum) ofscales. Recently, Owhadi has expanded upon a change-of-variables interpretation of homogenization, introducedby Kozlov, to devise accurate upscaling methods for somewave propagation (and other) problems in the presence ofa scale continuum. Binford has pointed out the relationbetween these ideas and immersed interface methods. Wereview these concepts and discuss extension to discontinu-ous Galerkin methods.

William Symes, Xin WangRice Universitysymes@caam.rice.edu, wangxin.tom@caam.rice.edu

MS61

Multiscale Aspects of Waveform Mismatch Mea-surements

We consider the inference of medium velocity from trans-mitted acoustic waves. Typically, the measurements aredone in a narrow frequency band. As a result the sensitiv-ity of the data with respect to velocity perturbations variesdramatically with the scale of the perturbation. ‘Smooth’perturbations will cause a phase shift, whereas perturba-tions that vary on the wavelength-scale cause amplitudevariations. We investigate how to incorporate this scaledependent behavior in the formulation of the inverse prob-

GS11 Abstracts 117

lem.

Tristan van LeeuwenDepartment of Earth and Ocean ScienceUniversity of British Columbia, Vancouver BC Canadatristan.vanleeuwen@gmail.com

MS62

Black-box Optimization in the Oil Industry

Many optimization problems found in oil industry applica-tions present nonlinear cost function and constraints, bothvery often based on reservoir flow simulations. Because inmany occasions the simulation code is not easily accessi-ble, the use of invasive methodologies can be troublesome.In this talk we will describe a number of general black-box optimization algorithms, and we will illustrate theseapproaches by a number of example cases with practicalrelevance in the oil and gas industry.

David Echeverria CiaurriStanford Universityecheverr@stanford.edu

Obiajulu J IseborStanford UniversityDepartment of Energy Resources Engineeringoisebor@stanford.edu

Louis J DurlofskyDepartment of Energy Resources EngineeringStanford Universitylou@stanford.edu

MS62

Modeling the Injectivity-Gap Problem in the Well-bore during CO2 Injection into Low PressureReservoirs

Depleted gas reservoirs are appealing targets for CO2 se-questration and EGR. Low abundant pressure is advanta-geous but injection process is challenging. Injecting CO2in liquid phase may lead to dry-ice or hydrate formation.Published studies that use outflow performance tools with-out integration with the reservoir model may not be repre-sentative. In this work, we provide a comprehensive studyto model CO2 flow in the wellbore and the reservoir takinginto account the proper thermodynamics.

Hussein HoteitConocophillipshussein.a.hoteit@conocophillips.com

MS62

Recent Advances in Closed-loop Reservoir Man-agement

Abstract not available at time of publication.

Jan Dirk JansenDelft University of Technology, andShell Exploration and Productionj.d.jansen@citg.tudelft.nl

MS62

Demonstration of the PEGrid Environment for Un-certainty Based Optimization of Subsurface Reser-

voirs

The uncertainty based optimization for multiple realiza-tions in reservoir modeling is a promising approach forefficient management of depleting hydrocarbon reserves.The application is computationally intensive, multidisci-plinary and require proprietary standard data security.From the success through the TIGRE [Vadapalli et al.2008] project in supporting these requirements, we havecreated the Petroleum Engineering Grid (PEGrid) for fos-tering industry-academia-government partnerships. Thepromise and scope of this effort will be presented.

Ravi VadapalliTexas Tech Universityravi.vadapalli@ttu.edu

Alan SillHigh Performance Computing CenterTexas Tech Universityalan.sill@ttu.edu

Shameem SiddiquiDepartment of Petroleum EngineeringTexas Tech Universityshameem.siddiqui@ttu.edu

Mohamed SolimanDepartment of Petroleum EngineeringTexas Tech University, Lubbock, TX 79409-3111mohamed.soliman@ttu.edu

Franz DeimbacherSchlumberger Information SolutionsHouston, TXfdeimbacher@slb.com

MS63

Current Research in Heavy Oil Modeling

While mathematical modeling has been successful in therecovery of conventional oil, it is still in the early stageof heavy oil modeling. As conventional oil reserves dwin-dle and oil prices rise, heavy oil is now the center stage.Enhanced heavy oil recovery methods are an intensive re-search area in the oil industry, and have recently generateda battery of recovery methods in what is the largest grow-ing sector of this industry, such as steam assisted grav-ity drainage (SAGD) and cyclic steam stimulation (CSS).However, the environmental impacts of these processes andthe use of a high volume of water and natural gas suggestthat extensive research is required for economic and en-vironmentally friendly development of heavy oil reserves.This presentation will give an overview on current researchin heavy oil modeling, and the presenter will also describehis current research program.

Zhangxin ChenUniversity of Calgaryzhachen@ucalgary.ca

MS63

Simulations of Commercial-scale Polymer Injectionusing a Parallel Computational Framework

A comprehensive polymer flow model has been imple-mented in the multiphase flow and reactive module of par-allel reservoir simulator (IPARS). An efficient time split-ting algorithm is used to solve the flow and transport equa-

118 GS11 Abstracts

tions independently. Large commercial scale polymerfloodsimulations are performed on multiple processors. The re-sults of polymer flood simulations in heterogeneous reser-voirs and parallel scalability will be presented. The impactof grid sizes on polymer rheology near injection wells willbe discussed.

Mojdeh DelshadDepartment of Petroleum and Geosystems EngineeringThe University of Texas at Austindelshad@mail.utexas.edu

Changli YuanCenter for Subsurface ModelingThe University of Texas at Austinclyuan@mail.utexas.edu

Mary F. WheelerCenter for Subsurface ModelingUniversity of Texas at Austinmfw@ices.utexas.edu

MS63

Large Scale Reservoir Simulation

Giant reservoirs of Middle East contain substantial por-tion of the worlds total hydrocarbons. Accurate simula-tion of these reservoirs requires as many as billion cells.This is needed to obtain accurate numerical solution andalso utilize the available vast amount of seismic and engi-neering data( measurements).A billion cell parallel reser-voir simulator was presented in 2009.This paper discussesnew cases as well as new methods to build and analyze largereservoir models using technologies from the other indus-tries. Numerical examples include utilization of a fully im-plicit, black oil dual, porosity dual permeability billion cellreservoir simulator on worlds largest oil reservoir. Parallelperformance, scalability and distribution of computationalwork are discussed. Numerical accuracy, effect of grid sizeon the results as well as parallel scalability is presented.Growth of model size in time and future computationaldemand, projected new computing platforms for the giantreservoir models are discussed. In addition to the numeri-cal aspects, presentation will cover the usage of 3-D spatialcomputing based visualization with hand gestures to buildand analyze giant models. Discussion will also cover uti-lization of sound in model building and analyzing.

Ali H. DogruSaudi Aramco Oil Co.dogruah@aramco.com.sa

MS63

Domain Decomposition Approaches for ModelingMultiphysics Multiphase Flow in Porous Media

In this presentation we discuss applying algorithms basedon domain decompositions for treating multiphysics, mul-tiscale multiphase flow in porous media. Applicationsinclude contaminant transport, carbon sequestration andpolymer flooding.

Mary F. WheelerCenter for Subsurface ModelingUniversity of Texas at Austinmfw@ices.utexas.edu

MS64

Discretisation Issues Related to Tensorial RelativePermeabilities

For simulations of flow of transport in porous media, themobility term is commonly modeled as a scalar quantity,and it is treated by upstream weighting. However, tensorialrelative permeability fields (and thus tensorial mobilities)in general arise on all scales, as is seen in both labora-tory and field experiments. Here, we discuss the impactof tensorial relative permeability fields on control volumeschemes, and propose new discretisation approaches for theequations.

Eirik KeilegavlenUniversity of BergenEirik.Keilegavlen@uib.no

Annette StephansenCIPR / University of Bergenannette.stephansen@uni.no

Jan M. NordbottenDepartment of MathematicsUniversity of Bergenjan.nordbotten@math.uib.no

MS64

Optimal Flux Allocation for Streamline Simulation

Streamline simulation has gained acceptance in modernreservoir flow simulation, its principal benefit being reduc-ing the three-dimensional transport problem into a set ofindependent one-dimensional problems. A critical step instreamline simulation is the assignment of the cumulativewell flux to individual streamlines. The current approachgenerally introduces mass balance errors. In this work,we explore optimizing the flux allocation so as to mini-mize these errors. We apply our new approach to two-dimensional multi-well examples

Gunilla KreissUniversity of Uppsala, Swedengunillak@it.uu.se

Marco ThieleStreamsim Technologies/Stanford Universitythiele@streamsim.com

Margot GerritsenDept of Petroleum EngineeringStanford Universitymargot.gerritsen@stanford.edu

Brad MallisonChevron Energy Tech. Co.btmb@chevron.com

MS64

Using Helmholtz Decomposition to Optimize Nu-merical Methods for Transport in Porous Media

We investigate the use of Helmholtz decomposition to con-struct a fast solver for the transport equation. Our methodis based on separating the dynamics into different partswith different qualitative features. For each part we adaptthe numerical method to effectively exploit specific featuresof this part. Then the solvers are combined to a solver for

GS11 Abstracts 119

the complete system. The last part can be done for exam-ple by using our solvers as preconditioners for a traditionalmethod or in an operator splitting framework. The aim ofthis work is to demonstrate the use of Helmholtz decom-position in this setting.

Halvor M. NilsenSINTEFOslohnil@sintef.no

Jostein R. NatvigSINTEF IKTjostein.r.natvig@sintef.no

Knut-Andreas LieSINTEF ICT, Dept. Applied MathematicsKnut-Andreas.Lie@sintef.no

MS64

Numerical Methods for Coupled Flow and Trans-port

Simulation of coupled phenomena in subsurface sciencesis a challenge of complexity, both modeling and compu-tational. Despite inevitable simplifying assumptions, themathematical model should faithfully represent coupledprocesses, domains, phases, and components. A compu-tational algorithm that maintains these couplings at allintermediate steps is unlikely to be practical for large-scaleproblems. It is crucial to construct ‘smart’, robust algo-rithms that first decouple judiciously at intermediate steps,in order to perform efficient computations on parts of thelarger system, and then restore couplings upon iterativeconvergence. Such algorithms would attempt to find sub-systems that are weakly coupled in the full system, so thatneglecting these couplings in intermediate iterations woulddegrade convergence of the full system as little as possi-ble. The talk will present some examples that can serve asbackground for later presentations in this minisymposium.

Thomas F. RussellNational Science FoundationOfc. of Integrative Activitiestrussell@nsf.gov

MS65

Modeling Hydrogen-water Flow with HydrogenDissolution as a Problem with ComplementarityConstraints

In an underground nuclear waste disposal hydrogen will beproduced by the corrosion of the waste packets. This hy-drogen migrates with the underground water flow and ispartially dissolved. The problem is modeled as a water-gasflow nonlinear system of PDEs with complementarity con-straints. A nonsmooth Newton method is applied to solveour system. This method can be regarded as an Active setstrategy. Numerical examples will be presented to showthe ability of our solver.

Ibtihel Ben Gharbia, Jerome Jaffre, Jean Charles GilbertINRIA-Rocquencourtibtihel.ben gharbia@inria.fr, Jerome.Jaffre@inria.fr, jean-charles.gilbert@inria.fr

MS65

Hyperbolic Models for Two-phase Flows with Dis-continuous Capillary Pressure Fields

We consider an immiscible incompressible two-phase flowwithin a one dimensional porous medium made of two dif-ferent rocks. The capillary pressure is supposed to be con-stant in each subdomain, but is not neglected at the in-terface between both rocks. We show that the qualitativebehaviour of the corresponding hyperbolic scalar conserva-tion law with discontinuous flux function depends stronglyon the orientation of the gravity with respect to the cap-illarity at the interface. A convergent numerical scheme isthen proposed to approximate the unique solution to theproblem.

Clement CancesLab. Jacques-Louis LionsParis 5eme, Francecances@ann.jussieu.fr

MS65

Physical Continuity Conditions in HMFE Approxi-mation for Compositional Two-Phase Flow in Het-erogeneous Porous Media

A key point in modeling phase transition in multiphasecompositional flow is the choice of main variables for solv-ing the resulting system of PDEs. Unfortunately, in thecase of heterogeneous porous media, the ideal choice ofvariables for describing phase transitions is not the bestfor ensuring physical continuity conditions. We present amodification of the generalized HMFE approximation tohandle this difficulty.

Peter KnabnerFriedrich-Alexander University Erlangen-Nurenberg,GermanyDepartment of Mathematicsknabner@am.uni-erlangen.de

Estelle MarchandDepartment Mathematik, AM1Friedrich-Alexander-Universitaet Erlangen-Nuernbergmarchand@am.uni-erlangen.de

MS65

Generalized HMFE Approximation for Composi-tional Two-Phase Flow

Two-phase two-components flow with phase-exchange isconsidered. The presented model is reduced to a system oftwo conservation PDEs. Two main unknown fields x,y arechosen and all state variables are locally recovered from xand y by solving a double-complementarity problem. Thefluxes can be eliminated explicitely and static condensa-tion leads to a nonlinear system of equations dependent onLagrange multipliers for x,y at each time step.

Torsten MuellerUniversity of Erlangen-Nuremberg Department ofMathematicstmueller@am.uni-erlangen.de

MS66

Development of Upscaling Techniques for General-

120 GS11 Abstracts

Purpose Coarse-Scale Compositional Simulation

Upscaling of compositional simulation is challenging dueto the interaction of small-scale heterogeneity and phasebehavior. We present a framework to upscale two-phasemulti-component flow in compositional simulation. It isshown that the oil and gas phases are not at chemical equi-librium on coarser scales. This non-equilibrium behavioris modeled by upscaled thermodynamic functions, whichmeasure the difference between component fugacities. Wealso introduce upscaled flow functions to account for theeffects of compressibility.

Alireza IranshahrStanford Universityiranshah@stanford.edu

Denis VoskovEnergy Resources Engineering DepartmentStanford Univeristydvoskov@stanford.edu

Yuguang ChenChevron Energy Technology CompanyYChen@chevron.com

MS66

An Efficient Multiscale Finite Volume Methodfor Multiphase Flow in Heterogeneous FracturedPorous Media

The i-MSFVM is extended to include multiphase flow inheterogeneous fractured porous media using a hierarchicalapproach. Local fracture functions are introduced to accu-rately capture fractures at the coarse scale. Only one de-gree of freedom per fracture network appears in the coarsesystem and independent grids are employed for matrix andfractures. Important is that neither local grid refinementnor grid alignment are needed in this approach. Conver-gence of the method is investigated and shown for variousrepresentative cases.

Hadi Hajibeygi, Dimitrios Karvounis, Patrick JennyInstitute of Fluid DynamicsETH Zurichhajibeygi@ifd.mavt.ethz.ch, karvounis@ifd.mavt.ethz.ch,jenny@ifd.mavt.ethz.ch

MS66

Upscaling Technique for Modeling of Well-Reservoir Interaction

The complexity of the interaction between the well and thereservoir depends strongly on the way the well region is iso-lated from the reservoir region. In this work we present theconcept of expanded well model, where the well region isgeometrically expanded to include the relevant part of thereservoir. The effectiveness of this technique is illustratedfor challenging problems such as fractured well and pro-duction from tight-gas reservoir.

Mohammad Karimi-FardStanfordkarimi@stanford.edu

Lou DurlofskyEnergy Resources Engineering DepartmentStanford Universitylou@stanford.edu

MS66

Adaptive Multiscale Finite-Volume Method forGravity Instability

The standard Multiscale Finite Volume (MsFV) methodfails to accurately reproduce finger evolution since smallerrors grow in time in unstable flow regimes. The itera-tive MsFV method overcomes this issue at the expenses ofcomputational efficiency. Here we introduce an adaptiveiMsFV technique that resolves local problems only in ar-eas close to the unstable front. In this context, the iMsFVmethod can be seen as an adaptive grid-refinement tech-nique.

Rouven Kuenze, Ivan LunatiUniversity of Lausannerouven.kunze@unil.ch, ivan.lunati@unil.ch

MS67

Application of Advanced Unstructured GriddingTechniques to Reservoir Simulation

Prismatic grids constructed by projection of a 2D grid canresolve stratigraphic layers and are well suited for high as-pect ratios of reservoir dimensions. In this talk, we addresschallenges of choosing a projection technique applicable tostructurally complex models with fault surfaces deviatingfrom vertical. We use topological parametric space of a ge-ologic model as a pre-image for prismatic grid generation,and further reduce limitations of prismatic grids in resolv-ing 3D geometries and property distributions by utilizinga zonal gridding strategy.

Larisa V. BranetsExxonMobil Upstream Research Companylarisa.v.branets@exxonmobil.com

Elena Kartasheva, Olga Kroshkina, Valeriy Kubyak,Valeriy ShmyrovNeurOKkartasheva@aconts.com, kroshkina@aconts.com,kubyak@aconts.com, shmirov@aconts.com

Xiao-Hui WuExxonMobil Upstream Research Companyxiao-hui.wu@exxonmobil.com

MS67

The UVT Transform: A Unified Approach toReservoir Modeling and Uncertainty Assessment

Current reservoir modeling practices revolve around theconstruction of a single 3D grid that is used for both dis-tributing reservoir properties and simulating fluid flow.The most common types of grid structure used have limita-tions in terms of the complexity of the reservoir structurethat they can represent and often require distortions of theindividual grid cells that impact both the spatial distri-bution of properties and numerical results of flow simula-tion. The UVT Transform has been introduced to enablea 3D transformation from today s space into the paleo-geochronological domain. Fit for purpose grids are con-structed in the transformed space alleviating structurallimitations and artificial cell deformations. This unifiedapproach ensures consistency between seismic and geolog-ical interpretation and the various representations of thesubsurface optimized for petrophysical property modeling,

GS11 Abstracts 121

fluid flow simulation or geomechanical studies.

Emmanuel Gringarten, Jean-Laurent MalletParadigmemmanuel.gringarten@pdgm.com,jean-laurent.mallet@pdgm.com

MS67

Upgridding by Amalgamation: Flow-AdaptedGrids for Multiscale Simulations

We discuss the creation of flow-adapted grids by amal-gamating cells from an original fine grid, using cell-wiseindicator functions to guide the amalgamation directionsand the new grid resolution. We present an algorithmicframework with a set of modular components that can becombined in different ways to create fit-for-purpose grids,which can be used to develop highly efficient multi-fidelitytransport solvers accompanying multiscale flow solvers.

Knut-Andreas LieSINTEF ICT, Dept. Applied MathematicsKnut-Andreas.Lie@sintef.no

Jostein R. NatvigSINTEF ICTDept. Applied Mathematicsjostein.r.natvig@sintef.no

MS67

Gridding Diplomacy - Balancing Requirements

Grid construction for the complex geometries arising inreservoir modelling can be regarded as an act of diplo-macy, where multiple requirements have to be balanced.For most practical applications, corner-point grids havebeen the preferred solution, applicable to both geologicalmodelling and dynamic flow simulations. The presenta-tion will discuss how conflicting requirements are balancedin current state-of-the-art gridding technology. Exampleswill be presented, illustrating challenges and solutions fromfield applications.

Tor Barkve, John NeaveRoxartor.barkve@roxar.com, john.neave@roxar.com

MS68

Rifting and Diking

Abstract not available at time of publication.

Roger BuckLamont-Doherty Earth ObservatoryColumbia Universitybuck@ldeo.columbia.edu

MS68

A Study on the Influence of the 2008 WenchuanEarthquake on the Stability of the Qinghai-TibetPlateau Tectonic Block System

In this paper, the 3D Finite Element Method was combinedwith a Discontinuous Deformation Analysis (DDA+FEM)to study the influence of the Wenchuan earthquake onthe stability of the tectonic blocks system of the Qinghai-Tibet Plateau under the background of northward extru-sion of the Indian Plate and obstruction of the strong crust

of the Sichuan basin. With constraints from GPS dataand focal mechanisms, we first calculated the velocity andstress fields of the region. Then, we numerically simu-lated the rupture process of the seismogenic fault of the2008 Wenchuan earthquake in overthrust form with a rightstrike-slip component. We then studied the movementand deformation of the tectonic blocks that was caused bythe earthquake and its influence on the stress state of theboundary faults. The numerical simulation indicates thatthe large earthquake causes the most tectonic blocks in thestudy zone at approximately a 1-mm deviation toward thenortheast; in particular, the Wenchuan seismogenic faultobviously deviated eastwards, and the maximum devia-tion reaches 1.5 m. It seems that the large earthquakecauses the Bayankala block at the west side of the Long-menshan fracture zone to extend farther eastward. TheWenchuan earthquake causes the Coulomb failure stresseson the boundary faults of the tectonic blocks in the studyzone to change to different extents. The maximum changeof the Coulomb failure stress reaches about 0.2 MPa atboth ends of the Wenchuan seismogenic fault, the southsection of the Xianshuihe fracture zone and part of thesoutheast section of the Dongkunlun fracture zone in theupper crust. Additionally, the Coulomb failure stresses alsoincrease to different extents between 0.01 and .02 MPa inregions such as the southernmost end of the Xianshuihefracture zone, part of the southeast section of the Dongkun-lun fracture zone, the southwest and southeast edges of theEerdos block, just to name a few.

Zuan ChenInstitute of Geology and GeophysicsChinese Academy of Scienceszachen@mail.igcas.ac.cn

MS68

Rifting and Faulting

Abstract not available at time of publication.

Eunseo ChoiLamont-Doherty Earth ObservatoryColumbia Universityechoi@ldeo.columbia.edu

MS68

GAMR: A Free Paralell Adaptive Tectonics andMantle Convection Code

The Computational Infrastructure for Geodynamics (CIG)has begun development of Gamr: a new community codefor tectonics and mantle convection. The principle newimprovement of Gamr over existing community codes suchas CitcomS and Gale is the use of parallel adaptive meshrefinement (AMR) to better resolve fine features such asfaults, plate boundaries, and mantle plumes. I will discussthe current status of Gamr and outline future milestones.

Walter LandryGeological and Planetary SciencesCalifornia Institute of Technologywalter@geodynamics.org

MS69

On Conservative Remapping Transport Schemesusing Icosahedral-hexagonal Grids

A high order incremental remapping scheme has beendesigned using the Icosahedral-hexagonal meshes. The

122 GS11 Abstracts

scheme has been tested for the advection of smooth scalarfields in both deformational and non-deformational flowfields. The incoming flux areas are approximated by greatcircle arcs using exact analytical trajectories. The bi-quadratic reconstruction functions are computed on projec-tion space to approximate the tracer field. The overall or-der of a transport scheme is thus determined completely byaccuracy of reconstructed tracer field and geometry of theflux areas. A comparison of errors due to reconstructionfunctions obtained by weighted least squares fits to pointvalues versus area-averaged values will presented. Also thevarious simplifications to the shapes of flux areas have beenanalyzed. A comparison of loss in accuracy due to simpli-fication of flux area geometry with respect to the gain incomputation efficiency will be presented. Finally the effectof three very different limiters: Flux corrective transport,Multi dimension flux and multidimensional extension ofvanLeer limiting will be presented.

Rashmi MittalNCARBoulder, CO, USAmittal@ucar.edu

Peter H. LauritzenNCARCGDpel@ucar.edu

MS69

A 2D Non-Hydrostatic Atmospheric Model Basedon a Non-Oscillatory Finite-Volume Method

Non-hydrostatic atmospheric modeling based on the finite-volume methods is becoming increasingly popular for theweather and climate simulations. A new two-dimensionalnon-hydrostatic model (compressible Euler system) hasbeen developed. A semi-discrete central finite-volumemethod is used for the spatial discretization, and timeintegration relies on explicit Runge-Kutta method. Thescheme does not employ expensive Riemann solvers andcharacteristic decomposition or any staggered grid system;and is computationally efficient. The non-oscillatory re-construction removes spurious oscillations, and improvesthe quality of numerical simulations. The model is testedfor various non-hydrostatic benchmark test-cases, and theresults will be presented in the seminar.

Ram NairNCARInstitute for Mathematics Applied to Geosciencesrnair@ucar.edu

MS69

A Flux-based Characteristicsemi-Lagrangian Method for Atmopspheric Mod-eling

Abstract not available at time of publication.

Matthew NormanNorth Carolina State UniversityRaleigh, NCmatthew.ross.norman@gmail.com

MS69

A Family of High-Order Finite-Volume Schemes for

Simulating Atmospheric Flows

We present our ongoing research on developing a setof numerical methods for simulating atmospheric flows.We have harnassed a high-order unstaggered finite-volumebased approach in developing a family of both advectiveand shallow-water models on the cubed-sphere and veri-fied our results against existing test cases. This approachhas been shown to satisfy a relatively weak CFL conditionand leads to more accurate results for the same order-of-accuracy, as compared with Galerkin-based approaches.

Paul UllrichUniversity of Michiganpaullric@umich.edu

Christiane JablonowskiUniversity of MichiganAnn Arbor MI 48109-2143cjablono@umich.edu

MS70

Shaping Regularization in Geophysical InverseProblems

Shaping regularization is a general method for imposingconstraints on the estimated model in the process of solv-ing an inverse problem. In the shaping framework, regular-ization enters the inverse problem in the form of a model orshaping operator, which maps the estimated solution intothe space of admissible solutions. Although this frame-work does not explicitly involve optimization, a connectionwith the optimization framework can be established via thetheory of proximity operators. Shaping regularization hasbeen applied to a wide range of geophysical problems, fromseismic velocity estimation to adaptive filtering, definitionof local seismic attributes, and time-frequency analysis. Iwill describe both the general theory and the known appli-cations.

Sergey FomelUniversity of Texas at Austinsergey.fomel@beg.utexas.edu

MS70

DG-based, UQ-equipped, Parallel, Adaptive, Scal-able Elastic-acoustic Seismic Inversion

We describe mathematical and computational issues under-lying an effort to create a new generation seismic inversioncode. These include: elastic-acoustic coupling, discontin-uous Galerkin discretization, gradient and Hessian consis-tency, parallel adaptivity on forest of octree meshes, uncer-tainty quantification via Bayesian inference, and scalabilityto petascale systems. Illustrations from global seismologyare provided.

Tan Bui-Thanh, Carsten BursteddeThe University of Texas at Austintanbui@ices.utexas.edu, carsten@ices.utexas.edu

Omar GhattasUniversity of Texas at Austinomar@ices.utexas.edu

James R. MartinUniversity of Texas at AustinInstitute for Computational Engineering and Sciencesjmartin@ices.utexas.edu

GS11 Abstracts 123

Georg Stadler, Lucas WilcoxUniversity of Texas at Austingeorgst@ices.utexas.edu, lucasw@ices.utexas.edu

MS70

A Fresh Look at Simultaneous Source

Many parameter estimation problems involve with aparameter-dependant PDEs with multiple right hand sides.The computational cost and memory requirements of suchproblems increases linearly with the number of right handsides. For many applications this is the main bottleneck ofthe computation. In this talk we show that problems withmultiple right hand sides can be reformulated as stochasticoptimization problems that are much cheaper to solve. Wediscuss the solution methodology and use the direct currentresistivity as a model problem to show the effectiveness ofour approach.

Eldad HaberDepartment of MathematicsThe University of British Columbiahaber@math.ubc.ca

MS70

Seismic Volume Reconstruction Via MultilinearRank Reduction

Consider a matrix S(n, m) where some entries are miss-ing. For instance, the entries S(m, n) can be the scoresassigned by buyer m to product n. Because not all buy-ers have bought and scored all products, the matrix con-tains empty entries. The goal of Collaborative Filtering(CF) is to predict the empty entries and therefore, predictproducts that a consumer might like. Seismic data recon-struction can also be interpreted as a matrix completionproblem similar to those arising in the field of CF. Seismiccompletion, however, entails reconstructing a 5D volume (atensor). Similar to the matrix completion problem, tensorcompletion can be achieved via rank reduction methods.The intention of this talk is to present our recent researchin rank reduction methods for seismic data reconstructionand de-noising. We will discuss some of challenges thatone needs to solve in order to create industrial-strengthalgorithms for multilinear seismic data processing.

Mauricio D. SacchiUniversity of Albertamsacchi@ualberta.ca

MS71

Model Reduced Variational Data Assimilation forReservoir Models

Variational data assimilation or ”the adjoint method” hasbeen used very often for model calibration problems inreservoir models. This method however requires the im-plementation of an adjoint model. Even with the use ofthe adjoint compilers that have become available recentlythis is a tremendous programming effort. Therefore wepropose another approach to variational data assimilationusing model reduction that does not require the implemen-tation of the adjoint of the original model. Model reducedvariational data assimilation is based upon a POD (ProperOrthogonal Decomposition) approach to determine a re-duced model for the original reservoir model. Once thisreduced model is available, its adjoint can be implementedvery easily and the minimization process can be solved

completely in reduced space with negligible computationalcosts. In many reservoir models the adjoint states can becomputed relatively easy and only the Jacobians with re-spect to parameters are hard to obtain. This makes a bal-anced POD-based method very attractive.

Arnold HeeminkDelft University of Technologya.w.heemink@ewi.tudelft.nl

Malgorzata KaletaShellm.p.kaleta@tudelft.nl

MS71

Parameter Identification for a Coupled Fluid Flowand Geomechanical Deformation Model

We present an application of iterative regularization fordata inversion from a coupled single-phase flow and aporoelastic reservoir. Production data and measurementsof surface deflection are inverted to reconstruct petrophysi-cal and elastic properties of the reservoir. By means of syn-thetic experiments we evaluate the contribution of surfacedeformation data in the estimation of uncertain proper-ties. Our evaluations can be potentially applied to designcost-efficient InSAR and GPS configurations for optimalmonitoring of reservoirs.

Marco IglesiasCivil and Environmental EngineeringMITmarcoi@mit.edu

Dennis McLaughlinCivil Engineering MITdennism@mit.edu

MS71

The Large Dimensional Bayesian Inversion Proemwith Application to a Reservoir Model

Petroleum reservoirs are complex geological formation en-compassing a wide range of physical and chemical hetero-geneities. These heterogeneities span over multiple lengthscales and are impossible to describe in deterministic detail.Geostatistics and, more specifically, stochastic modeling ofreservoir heterogeneities are being increasingly consideredby reservoir analysts and petroleum engineers for their po-tential in generating more accurate reservoir models to-gether with usable measures of spatial uncertainty. Thegoal of reservoir characterization is to provide a numeri-cal model of reservoir attributes such as hydraulic conduc-tivities (permeability), storativities (porosity) etc.. Theseattributes are then used as inputs into complex transferfunctions represented by various flow simulators to fore-cast future reservoir performance and oil recovery poten-tial. Permeability is one of the most important quanti-ties for prediction of fluid flow pattern.The estimation ofpermeability fields is therefore, critical and necessary forthe prediction of the behavior of contaminant plumes inaquifers and the production of petroleum from oil fields.In this paper, we employ a Bayesian hierarchical modelto quantify the uncertainty by formulating the posteriordistribution of the fine-scale permeability field conditionon both the coarse-scale data and production data andthe observed fine-scale data at the well locations. To rep-resent the spatial dependence in the permeability fields,Karhunen-Loeve expansion is used to reduce the number

124 GS11 Abstracts

of parameters. We assume the number of terms in thisexpansion is unknown and develop a two stage reversiblejump based MCMC algorithm to efficiently explore the pos-terior distribution. Furthermore, we introduce a multiscaledata integration method with upscaling technique for spa-tial modeling of the permeability. Numerical results arepresented by analyzing simulated as well as real data.

Bani MallickDepartment of StatisticsTexas A&M Universitybmallick@stat.tamu.edu

MS71

Bayesian Uncertainty Quantification for Flows inHeterogeneous Subsurface Formations

We study the uncertainty quantification for flows in het-erogeneous porous media. The permeability field is as-sumed to have channelized structure that are representedusing level sets approaches. In particular, the parameteri-zation of the channel boundaries is represented via the pa-rameterization of velocity field in the level sets equations.The truncation in the parameter space introduces errors inthe posterior measure that are investigated. Multi-stageMCMC algorithms are used for efficient sampling from theposterior. We present numerical results. This is a jointwork with Y. Efendiev, A. Mondal, B. Mallick, and A.Datta-Gupta.

Jia WeiTexas A and Mjwei@math.tamu.edu

MS72

Simulation of CO2 Migration Using Vertical Equi-librium Models

Recently, methods based on an assumption of vertical equi-librium (VE) has obtained renewed interest in the con-text of modeling CO2 migration over long time- and spa-tial scale. It is expected that after the injection period,CO2 will migrate over several kilometers in the horizon-tal direction, but only tens of meters in the vertical di-rection limited by the vertical boundaries of the aquifer.When the horizontal to vertical time scale becomes large,it is reasonable to approximate CO2 migration using ver-tically averaged models. The fact that VE-methods re-duces the spatial complexity of the problem from 3D to 2Dmay give important savings in computational time. Fur-thermore, because of improved vertical resolution the VE-approximation in many situations gives better solutionsthan standard 3D formulations. In this presentation weshow results from field simulations taken from the Utsiraand Johansen formation in the North Sea.

Helge K. DahleUniversity of Bergen, NorwayDepartment of Mathematicsreshd@mi.uib.no

MS72

Model Coupling for CO2 Sequestration Scenarios

Models for CO2 storage need to be able to describe non-isothermal, multiphase and compositional processes. How-ever, in most cases it is not necessary to describe all thephysical processes for the whole simulation time period.It is possible to describe a certain time scale with models

of reduced/adapted complexity. By coupling these mod-els of reduced complexity the model efficiency is increasedwithout neglecting the relevant phenomena.

Bernd FlemischUniversity of Stuttgart, Germanybernd.flemisch@iws.uni-stuttgart.de

MS72

A Multiphysics Approach for the Simulation ofMultiphase Flow Processes in Porous Media

The contamination of the unsaturated zone with a lightnon-aqueous phase liquid is studied, corresponding to adomain with randomly distributed heterogeneities wherecomplex three-phasethree-component processes are rele-vant only in a small (local) subdomain. This subdomainneeds fine resolution as the complex processes are governedby small-scale effects. For a comprehensive fine-scale modeltaking into account three-phasethree-component processesas well as heterogeneities in the whole (global) modeldomain, data collection is expensive and computationaltime is long. Therefore, we developed a general con-cept where on the one hand, the global flow field influ-ences the local three-phasethree-component processes onthe fine-scale. On the other hand, a coarse-scale satura-tion equation is solved where the effects of the fine-scalemulti-phasemulti-component processes in the subdomainare captured by source/sink terms and the effects of fine-scale heterogeneities by a macrodispersion term.

Rainer HelmigIWS, University of Stuttgart, GermanyInstitut fur Wasserbaurainer.helmig@iws.uni-stuttgart.de

MS72

Finite Volume Discretization of Multiphase PorousMedia Flows for CO2 Geological Sequestration

This talk deals with the simulation of multiphase compo-sitional Darcy flow for CO2 injection in saline aquifer. Itwill focus on the finite volume discretization of both Darcyfluxes and transport terms. The efficiency of the algorithmsis illustrated on near well CO2 injection test cases includ-ing dissolution of CO2 in the water phase, drying of thenear well region and salt precipitation.

Roland MassonInstitut francais du petroleroland.masson@ifp.fr

Cindy GuichardIFP Energies Nouvellescindy.guichard@ifp.fr

Robert EymardUniversity Paris Eastrobert.eymard@univ-mlv.fr

MS73

A Non-linear Correction and Maximum Princi-ple for Diffusion Operators Discretized using Cell-centered Finite Volume Schemes

In the present work, we propose a nonlinear correctionwhich gives nonoscillating solutions and which can be ap-plied to standard cell-centered finite volume schemes. Us-

GS11 Abstracts 125

ing an analytical solutions, we show the robustness and theaccuracy of this algorithm in comparison with results ob-tained by linear finite volume schemes which do not satisfythe minimum principles on this test.

Christophe Le PotierCEAGif sur yvetteclepotier@cea.fr

MS73

The Finite Volume Scheme Preserving MaximumPrinciple for Diffusion Equation

We construct a new nonlinear finite volume scheme fordiffusion equation on polygonal meshes and prove thatthe scheme satisfies the discrete extremum principle. Ourscheme is locally conservative and has only cell-centeredunknowns. Numerical results are presented to show howour scheme works for preserving discrete extremum princi-ple and positivity on various distorted meshes.

Zhiqiang ShengUniversite Pierre et Marie Curie - Paris VIsheng@ann.jussieu.fr

Guangwei YuanInstitute of Applied Physics and ComputationalMathematicsyuan guangwei@iapcm.ac.cn

MS73

Monotone Subfamily of Mimetic Finite DifferenceDiscretization Methods

The family of the Mimetic Finite Difference (MFD) meth-ods provides flexibility in the choice of parameters whichdefine a particular member of the family. The correctchoice of these parameters may guarantee that the resultinglinear numerical scheme satisfy the DMP principle. Themonotonicity limits of MFD method are investigated inseveral practically important cases including meshes gener-ated using the Adaptive Mesh Refinement (AMR) strategy.

Gianmarco ManziniIstituto di Matematica Applicata e TecnologieInformatichePavia, Italygm.manzini@gmail.com

Daniil Svyatskiy, Konstantin LipnikovLos Alamos National Laboratorydasvyat@lanl.gov, lipnikov@lanl.gov

MS74

Generalized Continua for Reinforced Geomaterials

The effective behaviour of soft elastic materials periodicallyreinforced by stiff slender elastic inclusions is investigatedthrough the homogenization method of periodic media. Alarge stiffness contrast induces a full coupling between thebeam behaviour of the inclusions and the shear behaviourof the matrix. Instead of the Cauchy continua usually ob-tained for homogenized composites, the macro behaviouris of second gradient type at the leading order, and differs

from that of Cosserat media.

Claude BoutinUniversite de Lyon- Ecole Nat. des Travaux Publics del’EtatDGCB - CNRS 3237Claude.BOUTIN@entpe.fr

Jean Soubestreuniversite de Lyon- ENTPECNRS 3237jean.soubestre@entpe.fr

MS74

Some Theoretical and Numerical Problems Relatedto the Modeling of Strain Localization by SecondGradient Continuum Theory

Generalized theories of continuum mechanics,as Cosserat’s, micromorphic or, with regards to this pre-sentation, second grade theories, have proven efficient tomodel the post strain localization behaviour of non-elasticmedia which the classical Cauchy’s theory cannot do prop-erly. The purpose of this presentation is to expound sometheoretical and numerical results related to strain loaliza-tion and second grade computations as analytical evidenceof localization, analytical solutions for second grade elasticproblems, locking in FE computations.

Denis CAILLERIE, Rene ChambonLaboratoire 3SRUniversit’e de Grenobledenis.caillerie@grenoble-inp.fr,rene.chambon@grenoble-inp.fr

MS74

Micromechanics of Ductile Porous Geomaterialswith Account of Pressure Sensitivity.

D. KONDO : Institut D’Alembert, UMR 7190, CNRS,UPMC, Paris,

J. LIN : University of Strasbourg, Department of Civil En-gineering, Strasbourg,

W. SHEN and J-F. SHAO : LML, UMR 8107, CNRS,USTL, LillePorosity strongly affects the overall ductile behavior of co-hesive geomaterials undergoing plastic deformation. In thepresent study, we propose an original micromechanical ap-proach which suitably couples Drucker-Prager type plastic-ity and evolving porosity under general triaxial loadings.The resulting model has the advantage to be based on asingle macroscopic yield function which also plays the roleof plastic potential. It is shown that this yield function isparticularly appropriate to account for the voids collapseand plastic shearing mechanisms which govern the mechan-ical behavior of various porous geomaterials.

Djimedo KondoUniversite Pierre et Marie Curiedjimedo.kondo@upmc.fr

MS74

Darcy Vs Brinkman

Different filtration laws have been proposed in history to

126 GS11 Abstracts

describe a fluid flow through porous medium. We focushere on Darcy’s law

�v = K(f −∇p)

and Brinkman’s law

B�v + ∇p − μΔ�v = f .

Using the method of homogenization we derive both laws,in case of porous medium with special structure. The goalof this work is to compare the two laws and see that theycan be related with an appropriate choice of parameters.

Eduard Marusic-PalokaDepartment of Mathematics,University of Zagreb, Croatiaemarusic@math.hr

MS75

Super-resolution in Time-reversal by Homogeniza-tion

Over the past decades, much attention has been devotedto the detection of small inhomogeneities in materials ortissues, using non-invasive techniques, primarily electro-magnetic wave-fields. The characterization of the signa-ture of small inclusions is now well understood. But manyquestions remain regarding their accurate localisation, es-pecially in non-homogeneous media. In contrast, duringthe same period it was shown that inhomogeneous mediaare more favorable than homogeneous ones for time rever-sal experiments, involving active sources. This talk will bedevoted to recent results on the enhanced resolution avail-able in structured media, and their consequences for theimaging of small inhomogeneities.

Yves CapdeboscqMathematical Institute, University of Oxfordyves.capdeboscq@maths.ox.ac.uk

MS75

Homogenization Effects in Domains with Oscillat-ing Boundaries

We consider domains with microinhomogeneous bound-aries. We study the asymptotic behavior of solutions toboundary value problems in domains with rapidly oscillat-ing or rough boundaries and in multilevel and cascade thickjunctions with rapidly oscillating transmission zone. In-homogeneous Fourier boundary conditions with perturbedcoefficients are set on the oscillating boundaries. We provethe homogenization theorems and convergence of energyintegrals as the small parameter characterizing the microin-homogeneity, tends to zero. It is shown that there are sev-eral qualitatively different cases in the asymptotic behaviorof the solutions.

Grigory A. ChechkinDepartment of Differential EquationsMoscow Lomonosov State University, Moscowchechkin@mech.math.msu.su

Tatiana P. ChechkinaMoscow Engineering Physics InstituteNational Research Nuclear Universitychechkina@mail.ru

MS75

Representation Formulas for L∞ Norms of Weakly

Convergent Sequences of Gradient Fields in Ho-mogenization

We identify local representation formulas that in the finephase limit provide upper bounds on the limit superior ofthe L∞ norms of gradient fields inside homogenized porousmedia. The local representation formulas are expressed interms of the weak limit of the gradient fields and local cor-rector problems. The upper bounds may diverge accordingto the presence of rough interfaces. We identify explicitlocal formulas for the limit of the L∞ norms of the asso-ciated sequence of gradient fields inside smooth periodicmicrostructures.

Robert P. LiptonDepartment of MathematicsLouisiana State Universitylipton@math.lsu.edu

Tadele MengeshaLouisiana State UniversityDepartment of Mathematicsmengesha@math.lsu.edu

MS75

Homogenization of Pseudo-parabolic Systems

Pseudoparabolic systems with periodic data are homoge-nized to obtain upscaled limits. The limit is characterizedand convergence is established in various linear cases forboth the classical binary medium model and the highly-heterogeneous case. The limit of vanishing time-delay pa-rameter in either medium is included. The double-porositylimit of Richards’ equation with dynamic capillary pressureis included.

Ralph Showalter, Malgorzata PeszynskaDepartment of MathematicsOregon State Universityshow@math.oregonstate.edu,mpesz@math.oregonstate.edu

Son-Young YiUniversity of Texas at El Pasosyi@utep.edu

MS76

A Stochastic Approach to Modeling Effective Mul-tiphase Flows in Heterogeneous Porous Media

Heterogeneity and buoyancy can compete or combine to-gether to influence spreading in multiphase flows throughporous media. In this work we study the interaction ofthe two with the goal of deriving an effective large scaleequation that accurately quantifies the rate of spreading.To do so we work in a stochastic framework treating themedium permeability as random. In particular the rate ofspreading is quantified by an effective dispersion (and ef-fective permeability) coefficient. To validate the approachwe perform a series of numerical simulations, which showgood qualitative agreement. We find that the interplay be-tween density and heterogeneity leads to an enhancementof the front spreading as well as a renormalization of theevolution of the mean front position relative to an equiv-alent homogeneous medium. The quantification of thesephenomena plays an important role in several applications,including for example carbon sequestration and enhanced

GS11 Abstracts 127

oil recovery.

Diogo BolsterDepartment of Civil Engineering and Geological SciencesUniversity of Notre Damebolster@nd.edu

Marco DentzIDAEASpanish National Research Council (CSIC)marco.dentz@idaea.csic.es

Insa NeuweilerInstitute for Fluid Mechanics and Environmental Physicsin Cneuweiler@hydromech.uni-hannover.de

Jesus CarreraIDAEA, CSIC, Spainjcrgeo@idaea.csic.es

MS76

Nonlinear Transport Problems with Time-memoryEffects

Contaminant transport in heterogeneous porous materialscan be described by the convolution of a PDE with a time-memory kernel that accounts for the long correlations in-duced by the underlying flow. In this talk we will discusshow to extend this transport formalism to include non-linearities (e.g., geomechanical, and geochemical effects),what is the interplay between nonlinearities and memoryeffects, and what are the mathematical challenges associ-ated with the solution of such equations.

Andrea CortisEarth Sciences Division, 90-1116Lawrence Berkeley National Laboratoryacortis@lbl.gov

MS76

Efficient Solution of Advection-Reaction Diffusionwith Stochastic Forcing

We consider exponential based integrators for porous me-dia flow in two and three dimensions. These methods arebased on solving the linear problem exactly and exploit ef-ficient methods for computing large matrix exponentials.We are particularly interested in the effects of time de-pendent stochastic forcing. The forcing is taken to modelunknown movement between trapped and flowing solutes,unknown small scale variations in the reaction term or timedependent changes in permeability. We examine conver-gence and efficiency of new schemes for the stochastic PDEsfor both additive and multiplicative noise and present nu-merical results for realistic flow type problems.

Gabriel J. LordHeriot-Watt Universityg.j.lord@ma.hw.ac.uk

Antoine TambueHeriot Watt Universityat150@ma.hw.ac.uk

Sebastian GeigerHeriot-Watt UniversityEdinburgh

Sebastian.Geiger@pet.hw.ac.uk

MS76

Modeling Dispersion in Heterogeneous Porous Me-dia with Stochastic Diffusion Processes for FluidParticle Velocities

To model the dispersion of fluid particles induced by con-ductivity heterogeneity, we propose stochastic diffusionprocesses for the Lagrangian velocity of fluid particles.The corresponding processes are continuous in time andare able to accurately capture the dispersion behavior forlog-conductivity variances σ2

Y ranging from 0.06 . . . 4. Byvalidation with Monte Carlo data it is demonstrated thatthe model reproduces non-Gaussian velocity statistics andlong-term velocity correlation effects very accurately.

Daniel W. MeyerInstitute of Fluid Dynamicsmeyerda@ethz.ch

Patrick JennyInstitute of Fluid DynamicsETH Zurichjenny@ifd.mavt.ethz.ch

Hamdi TchelpiStanford Universitytchelepi@stanford.edu

MS77

High-resolution Modelling of Geodynamic andPlanetary Processes with Finite Differences andMarker-in-cell Techniques

Modern gross challenges in geodynamic and planetarymodelling are: (i) creating high-resolution realistic 3Dnumerical models applicable to nature, and (ii) obtain-ing a rigorous understanding of geodynamic and plane-tary processes and the key physical parameters control-ling them. One possible pragmatic strategy is to use acombination of conservative finite differences with markerin cell techniques on fully staggered rectangular Cartesiangrid. This approach allows for both simplicity of numeri-cal implementation and stability and robustness of numer-ical solutions. Possible drawback is in limited possibilityof grid refinement that can indeed be efficiently compen-sated by low memory requirements and high speed of com-putations allowing for high resolutions in both 2D (thou-sands of points in each direction with direct solvers) and3D (hundreds of points in each direction with multigridsolvers) by using only few CPUs. We developed a familyof finite-difference, marker-in-cell codes I2ELVIS/I3ELVISwhich can handle visco-(elasto)-plastic rheology, miner-alogical phase changes, free surface and (when needed)self-gravitation. With these tools we created a numberof predictive numerical models for various geodynamicand planetary processes, such as self-consistent mid-oceanrift formation with transform faults, oceanic and oceanic-continental subduction initiation and long-term evolution,continental collision with spontaneous slab breakoff, intru-sion emplacement into the crust, planetary accretion andmetallic core formation.

Taras GeryaGeophysical InstituteETH-Zurichtaras.gerya@erdw.ethz.ch

128 GS11 Abstracts

MS77

On Geothermal Processes within the Lithosphere

Most heat and fluid flow simulations for geothermal playscouple thermal and darcy flow at the reservoir scale, how-ever, non-conventional geothermal exploration requires cer-tainty of heat and fluid flow at depth over much largerscales. We demonstrate approaches to assimilating 3Dbasin (and beyond) geological provinces to simulations thatcapture meter scale coupled thermal - fluid flows. Theseinclude utilizing a material point approach to the finite el-ement method, a simplified PDE compositional language,SPH methods for geometry interpolation, simple forms ofmesh refinement, parallelization to 1000s of CPUs andsome of the benchmarks addressed.

Steve QuenetteVictorian Partnership for Advanced Computingsteve.quenette@monash.edu

John MansourVPACjmansour@vpac.org

Dave LeeMonash Universitydavid.lee@monash.edu

Louis MoresiSchool of Mathematical SciencesMonash Universitylouis.moresi@monash.edu

MS77

Positivity Preserving Well-balanced Methods forthe Shallow-water Equations

Shallow-water equations with a non-flat bottom topogra-phy have been widely used to model flows in rivers andcoastal areas. An important difficulty arising in these sim-ulations is the appearance of dry areas, and standard nu-merical methods may fail in the presence of these areas.These equations also have steady-state solutions in whichthe flux gradients are non-zero but exactly balanced by thesource term. In this presentation, we propose some recentlydeveloped high-order discontinuous Galerkin and weightedessentially non-oscillatory methods, which can preserve thesteady-state exactly, and at the same time are positivitypreserving without loss of mass conservation. Some nu-merical tests are performed to verify the positivity, well-balanced property, high-order accuracy, and good resolu-tion for smooth and discontinuous solutions.

Yulong XingDepartment of MathematicsUniveristy of Tennessee / Oak Ridge National Labxingy@math.utk.edu

MS77

High Order Interface Method for Solving Multi-flow Navier-Stokes Equations in Geophysics

We developed a second-order accurate interface method,based on the matched interface and boundary approach, tosolve the Navier-Stokes equations with discontinuous vis-cosity and density on non-staggered Cartesian grid. We de-rive for the first time the interface conditions for the inter-mediate velocity field and the pressure potential functionthat are introduced in the projection method. The differen-

tiation of velocity components on a stencil across the inter-face is aided by using the coupled fictitious velocity values,whose representations are solved by using the coupled ve-locity interface conditions. These fictitious values and thenon-staggered grid allow a convenient and accurate approx-imation of the pressure and potential jump conditions. Acompact finite difference method is adopted to explicitlycompute the pressure derivatives at regular nodes to avoidthe pressure-velocity decoupling. Numerical experimentsverify the designed accuracy of the numerical method. Ap-plications to geophysical problems demonstrate that thesharp pressure jumps on the clast-Newtonian matrix areaccurately captured for various shear conditions, moderateviscosity contrasts and a wide range of density contrasts. Itis also shown that a large absolute difference of the viscos-ity across the interface will cause the simulation unstable,due to the large transfer error in computing the jumps inthe pressure and potential interface conditions from thenumerical solutions of the velocity field.

Yongcheng Zhou, James LiuDepartment of MathematicsColorado State Universityyzhou@math.colostate.edu, liu@math.colostate.edu

Dennis HarryDepartment of GeosciencesColorado State Universitydharry@cnr.colostate.edu

MS78

A Semi-Implicit, Semi-Lagrangian, P-AdaptiveDiscontinuous Galerkin Method for the ShallowWater Equations

A semi-implicit and semi-Lagrangian DiscontinuousGalerkin method for the shallow water equations is pro-posed and analyzed. The method is equipped with a simplep-adaptivity criterion, that allows to adjust effectively thenumber of local degrees of freedom employed to the localstructure of the solution. Numerical results in the frame-work of one dimensional test cases prove that the methodcaptures accurately and effectively the main features of lin-ear gravity and inertial gravity waves, as well as reproduc-ing correct solutions in nonlinear open channel flow tests.The effectiveness of the method is also demonstrated by nu-merical results obtained at high Courant numbers and withautomatic choice of the local approximation degree. Per-spectives for extensions to geophysical flows applicationsare discussed.

Luca BonaventuraMOX Politecnico di MilanoMilan, Italy 20133luca.bonaventura@polimi.it

Marco RestelliPolytechnic University Milanmarco.restelli@polimi.it

Giovanni TumoloICTP, Trieste, Italygrumolo@ictp.it

GS11 Abstracts 129

MS78

Jacobian Free Efficient Implicit Solver for HOMME

Abstract not available at time of publication.

Kate EvansOak Ridge National Laboratoryevanskj@ornl.gov

MS78

CG/DG Formulation of the Non-Hydrostatic Uni-fied Model of the Atmosphere (NUMA)

We describe our progress in the development of a paral-lel 3D compressible Navier-Stokes model for use in non-hydrostatic atmospheric modeling. The explicit time-integration version of NUMA currently scales up to tensof thousands of processors but we would like to extend itto hundreds of thousands. We will describe our MPI im-plementation and challenges facing us in scaling the im-plicit solvers. NUMA is based on continuous and dis-continuous Galerkin methods (CG/DG) and is high-order(arbitrarily high-order polynomials can be used), fully un-structured, and capable of using explicit, semi-implicit, andfully-implicit time-integrators. Finally, NUMA can be usedboth for regional and global modeling. We will report onbenchmark test cases to show the accuracy and efficiency ofthe model and will discuss the many challenges remainingin the development of this model.

Francis X. GiraldoNaval Postgraduate Schoolfxgirald@nps.edu

James KellyDepartment of Applied MathematicsNaval Postgraduate Schooljfkelly@nps.edu

MS78

Quasi-Monotone Advection Methods for SpectralElements

High Order Method Modeling Environment (HOMME)is a spectral element dynamical core option in Commu-nity Earth System Model (CESM). The spectral elementmethod in HOMME is a forth-order accurate continuousGalerkin method on quadrilateral elements. In this talkwe discuss new quasi-monotone limiters for HOMME. Wecompare Zalesak-type FCT limiters with ones using opti-mal reconstruction. The optimal reconstruction is obtainedby solving a quadratic programming problem local to eachelement. To illustrate our ideas, we use divergent and non-divergent advection tests for geophysical flows with dis-tortive winds from the paper by Nair & Lauritzen, 2010.

Oksana GubaSandia National LaboratoriesNM, USA.onguba@sandia.gov

Mark A. TaylorSandia National Laboratories, Albuquerque, NMmataylo@sandia.gov

Amik St-CyrNational Center for Atmospheric ResearchInstitute for Mathematics Applied to the Geosciencesamik@ucar.edu

MS78

The Variable Resolution Spectral Element Dynam-ical Core in the Community Atmospheric Model(cam)

NCAR’s High Order Method Modeling Environment(HOMME) uses high-order element-based Galerkin meth-ods and the cubed sphere geometry to solve global PDEs onmassively parallel computers in a coordinate system thatis free of polar singularities. HOMME has been updated toallow static refinement via conforming quadrilateral meshesand this talk discusses the implementation of refinement inHOMME’s spectral element dynamical core as used by theCommunity Atmospheric Model (CAM-HOMME).

Michael N. LevySandia National LaboratoriesNM, USA.mnlevy@sandia.gov

James OverfeltSandia National Laboratoriesjroverf@sandia.gov

Mark A. TaylorSandia National Laboratories, Albuquerque, NMmataylo@sandia.gov

MS79

Title Not Available at Time of Publication

Abstract not available at time of publication.

Biros GeorgeWe have 13 speakers.Web-site does not let speaker field be blank.biros@seas.upenn.edu

MS79

Assimilation of Production and 4D Seismic Data inOil Reservoir Modeling by Virtual Sensing

Time-lapse (4D) seismic attributes can provide valuableinformation regarding the subsurface fluid flow. Thisspatially-rich source of information supplements the poorareal information attainable from production well data.While fusion of information from multiple sources holdsgreat promise, in practice, this task is far from trivial. Jointinversion is complex for many reasons, including dissimilartemporal and spatial scales, ambiguous coupling mecha-nisms between the various parameters, and unclear rela-tive statistical fidelity of the different data sources. Theseconcerns limit the applicability of many data-assimilationtechniques. Adjoint-based methods offer great efficiencyand consistency; however their implementation generallyrequires extensive coding effort. In this study we presenta formulation that exploits the adjoint functionality thatmodern simulators offer for production data, to consis-tently assimilate inverted 4D seismic attributes. The cen-tral idea is to incorporate seismic inverted attributes byvirtual sensors. These sensors mimic production wells andthereby leverage adjoint functionality for the seismic data.Precautions are taken to ensure that such sensors will notinterfere with the fluid dynamics. Other than the obvi-ous consistency advantage in the proposed methodology,its implementation does not require re-programming legacyadjoint code, and in principle can be utilized for the incor-poration of a broad range of data sources and attributes.We present numerical results demonstrating considerable

130 GS11 Abstracts

improvement in matching saturation distribution in differ-ent assimilation setups. This work was carried out as partof a joint Shell-IBM research project.

Lior HoreshBusiness Analytics and Mathematical SciencesIBM TJ Watson Research Centerlhoresh@us.ibm.com

Gijs van Essen, Eduardo JimenezShell Innovation Research & Developmentgijs.vanessen@shell.com,, eduardo.jimenez@shell@com

Sippe DoumaShellsippe.douma@shell.com

Andrew R. ConnIBM T J Watson Research Ctrarconn@us.ibm.com

Ulisses MelloIBM Watson Research Centerulissesm@us.ibm.com

Paul van den HoekShell Innovation Research & Developmentpaul.vandenhoek@shell.com

MS79

Joint Electromagnetic-Seismic Inverse Modeling

Seismic data are first transformed into the Laplace-FourierDomain, which changes the modeling of the seismic wavefield from wave propagation to diffusion. Several bene-fits follow: (1) seismic and EM data are better matchedin resolution, governed by the same physics of diffusion,(2) standard least squares inversion works well with dif-fusive type problems, and (3) possibilities to image acrossmultiple scale lengths, incorporating different types of geo-physical data and attributes.

Gregory NewmanLBLGANewman@lbl.gov

MS79

Including Multiply-Scattered Waves in SeismicImaging

Imaging the subsurface in exploration seismology con-ventionally only makes use of primaries (singly reflectedwaves). In certain circumstances, multiples (waves thatreflected more than once on the path from source to re-ceiver), can be used to form an image. This allows betterillumination of the bottom of subsurface structures, andnear-vertical features. A method for jointly imaging usingboth primaries and multiples to enhance the result, will bepresented.

Alan RichardsonDepartment of Earth, Atmospheric and PlanetarySciencesMassachusetts Institute of Technologyalan r@mit.edu

Alison MalcolmMIT

amalcolm@mit.edu

MS80

Data Assimilation Applications in Large Scale Re-servior Models

Abstract not available at time of publication.

Remus HaneaDelft University, Netherlandsr.g.hanea@ewi.tudelft.nl

MS80

Particle Ensemble Kalman Filtering with Applica-tion to a Reservoir Model

Abstract not available at time of publication.

Hussein HoteitConocophillipshussein.a.hoteit@conocophillips.com

MS80

Reservoir Applications of the Adaptive GaussianMixture Filter

The ensemble Kalman filter (EnKF) is currently consideredas a promising method for conditioning reservoir simulationmodels to production data. However, it has some short-comings in estimating the correct posterior distribution.An alternative that avoids some of these shortcomings isthe adaptive Gaussian mixture filter (AGMF) [Stordal et.al., 2010]. Here we will present a comparison between theEnKF and the AGMF on a well known test case, the PUNQS3 model. high-level commands.

Geir NvdalInternational Research Institute of Stavanger& Centre of Integrated Petroleum Research, UoBgeir.naevdal@iris.no

Andreas Stordal, Randi ValestrandInternational Research Instititue of Stavanger (IRIS)andreas.s.stordal@iris.no, randi.valestrand@iris.no

MS80

Multi-level Parallelization of Ensemble Kalman Fil-ter (EnKF) for Reservoir History Matching

The ensemble Kalman filter (EnKF) has been successfullyimplemented in parallel to assimilate data in reservoir his-tory matching problems. In the EnKF method, a suite ofreservoir models (set of ensemble members) runs indepen-dently forward in time (forecast step), and is continuouslyupdated as new data becomes available (assimilation step).An efficient implementation of the EnKF is presented inwhich three-level parallelization is employed. The first levelof parallelization is for the forecast step by running eachensemble member on a different computer processor. Thisis very efficient for a large number of ensemble members,but without additional parallization, the memory of a sin-gle processor constrains the size of the reservoir simulation.Therefore, a second level of parallelization which uses aparallel reservoir simulator for each realization is imple-mented. The assimilation step requires collecting a statevector from each ensemble member. If this data is collectedon a single processor, this poses an additional limitation onthe size of the EnKF problem in terms of both memory and

GS11 Abstracts 131

computation time. Therefore, we propose an algorithm inwhich a third level of parallelization is acheived for theassimilation step.

Reza TavakoliUT-Austintavakoli@ices.utexas.edu

Gergina PenchevaUniversity of Texas at Austingergina@ices.utexas.edu

Mary F. WheelerCenter for Subsurface ModelingUniversity of Texas at Austinmfw@ices.utexas.edu

MS81

Benchmarking Multiscale Mixed Finite ElementMethod (MsMFEM) for Modeling Flow Accuracyand Computational Efficiency

Multiscale Mixed Finite-Element method attempts tocapture sub-grid geological information directly into thecoarse-scale via mathematical basis functions. These ba-sis functions contain essential multiscale information andare coupled through a global formulation to provide highlyaccurate approximation of the flow solution. MsMFEM isused to simulate flow on highly heterogeneous geologicallyrealistic corner-point grids with faults and fractures. TheMsMFEM is benchmarked against a proprietary simula-tor and a fine-scale model for accuracy and computationalefficiency.

Mayur PalShell International Exploration and Production B.V.Rijswijk, The Netherlandsmayur.pal@shell.com

Sadok LamineShell International Exploration and Production B.V.sadok.lamine@shell.com

Faruk O. Alpak, Shell International Exploration & Production Inc., USAOmer.Alpak@shell.com

Ingeborg LigaardenSINTEFingeborg.ligaarden@sintef.no

Knut-Andreas LieSINTEF ICT, Dept. Applied MathematicsKnut-Andreas.Lie@sintef.no

MS81

Multiscale Simulation for Two-phase Flow inPorous Media

In this contribution we develop multiscale simulation ca-pabilities, with an emphasis on robustness in terms of gridirregularity and the duality between upscaling and precon-ditioning. We place particular emphasis on issues arising in3 spatial dimensions, including the use of secondary (non-conserved) coarse variables.

Jan M. NordbottenDepartment of Mathematics

University of Bergenjan.nordbotten@math.uib.no

MS81

Goal Ori-ented Upscaling for Coupled Flow/GeomechanicsSimulations

Abstract not available at time of publication.

Adolfo RodriguezConocoPhillipsadolgo.a.rodriguez@conocophillips.com

MS81

Incorporation of Diffusion into Compositional Mul-tiphase Flow Simulation

Mixing of nonequilibrium phases in both open space and inpermeable media is of fundamental nature with broad ap-plications in CO2 injection in hydrocarbon reservoirs andfor CO2 sequestration in saline aquifers, and measurementof diffusion coefficients. Despite the importance of mixing,the process has not been incorporated in current numericalreservoir simulators properly especially when one grid cellcontains one of the nonequilibrium phases and the neigh-boring cell contains the other phase. To be specific supposeone cell contains CO2 and the neighboring cell contains wa-ter or oil phase. Current reservoir models cannot accountproperly for the flux between the two grid cells. A fun-damental deficiency is that local equilibrium condition isnot imposed at the interface. Consequently current simula-tors give erroneous results even with fine gridding. In thiswork, for the first time we incorporate the criteria of lo-cal equilibrium at the interface between the neighborhoodgrid cells to account for diffusion flux and convective fluxproperly. We use a mixed finite element framework to ac-count for diffusion flux calculation both within a cell andinterface flux. As a result allowance is made for the con-ditions that interfacial diffusion flux is much higher thaninterfacial convective flux while bulk phase convective fluxis much higher than bulk phase diffusion flux. Two formu-lations are established, one for a moving interface and theother for a fixed interface. Our moving interface formu-lation is compared with open space formulation recentlypresented in another study. We also present a fixed meshmethod that is much faster and appropriate for reservoirsimulation. The efficiency of the fixed mesh method ismainly due to its larger time step size compared to themoving interface formulation. Except for CPU efficiency,the results from the two formulations are the same.

Shuyu SunDivision of Mathematical and Computer Sciences &EngineeringKing Abdullah University of Science and Technology(KAUST)shuyu.sun@kaust.edu.sa

Abbas FiroozabadiYale Universityabbas.firoozabadi@yale.edu

MS82

Optimization-based Postprocessing of Finite Ele-ment Solutions for Recovering Monotonicity

Loss of monotonicity and violation of the discrete maxi-

132 GS11 Abstracts

mum principle are typical drawbacks exhibited by the nu-merical solutions of the conventional approximation meth-ods, such as finite elements (FE), finite volumes (FV),and mixed finite elements. The problem is particularlyimportant in cases of highly anisotropic diffusion tensorsor distorted unstructured meshes. In this talk, we sug-gest a least-change correction to available FE solution. Itis aimed on recovering the monotonicity properties. Thispostprocessing procedure is based on solving a monotonicregression problem with some extra constraints. The post-processed solution preserves the accuracy of the discreteFE approximation in L2-norm, satisfies the discrete max-imum principle and meets the conservativity requirement.We present an algorithm for solving the postprocessingproblem. Its efficiency is demonstrated by the results ofnumerical experiments.

Oleg BurdakovLinkoping Universityolbur@mai.liu.se

Ivan KapyrinInstitute of Numerical Mathematics, RAS, Moscowkap-ivan@bk.ru

MS82

A Monotone Discretization Method for theConvection-Diffusion Equation

We present a non-linear monotone finite volume methodfor the numerical approximation of the steady convection-diffusion equation on unstructured meshes in two spatialdimension. The method is formally second-order accurateas the convection flux is evaluated numerically by meansof a piecewise linear reconstruction within each cell andat mesh vertices. Non oscillatory behavior in presence ofstrong gradients is achieved through suitable slope limitersin the solution. The edge gradients, required to discretizethe diffusive fluxes, are defined inside additional quadrilat-eral cells centered at mesh edges, the so-called ”diamondcells”, by a gradient formula which is formally exact forlinear solutions. A set of numerical results documents theperformance of the method in treating problems with in-ternal layers and solutions with strong gradients.

Gianmarco ManziniIstituto di Matematica Applicata e TecnologieInformatichePavia, Italygm.manzini@gmail.com

MS82

Monotone Finite Volume Discretization of Two-phase Black Oil Equations on Polyhedral Cells

A new monotone finite volume method with a nonlineartwo-point flux approximation is applied to the approximatesolution of two-phase black oil equations on 3D meshescomposed of polyhedral cells. In special cases of orthogo-nal grid with isotropic or grid-aligned anisotropic perme-ability tensor the linear and nonlinear approximations areidentical. In general case the linear two-point flux dis-cretization provides no approximation, whereas the non-linear two-point flux discretization is at least first orderaccurate. Numerical experiments with two-phase black oilmodel demonstrate that the quality of the discrete flux ap-proximation has a great effect on the front behavior and

the water breakthrough time.

Yuri VassilevskiInstitute of Numerical MathematicsRussian Academy of Sciencesyuri.vassilevski@gmail.com

Kirill NikitinRussian Academy of Scienceskirill.nikitin@gmail.com

Alexander DanilovInstitute of Numerical MathematicsRussian Academy of Sciencesa.a.danilov@gmail.com

MS83

A Multiscale Model for Thermo-hydro-mechanicalAnalysis of Porous Media and Constitutive Be-haviour Including Capillary effects

We propose a thermo-hydro-elastoplastic model for par-tially saturated three-phase soil. Averaging theory leadsfrom micro to macro level. Restrictions resulting fromthermodynamics are imposed thus the description of thebehavior at macro scale is thermo-dynamically consistent.Constitutive parameters are identified for a data concern-ing a see gas reservoir; capillary effects and micro collapsedue to variation of load and saturation are found as aninterpretation of a behavior observed at macro scale.

Marek LefikTechnical University of LodzDepartment of geotechnics and Engineering Structuresmarek.lefik@p.lodz.pl

Bernhard SchreflerDepartment of Construction and TransportationEngineering,University of Paduabas@unipd.it

MS83

Chemical Local Non-equilibrium: Origins, Mod-elling and Analysis

Transport of chemical species in heterogeneous geomateri-als during the transient phase is very often characterizedby the local non equilibrium conditions. In this presenta-tion the different origins of such conditions and their conse-quences on the macroscopic behaviour, are reviewed. Par-ticular attention is paid to the chemical heterogeneity ofthe geomaterial. In the second part, modelling by homoge-nization of the transport in a double porosity medium, in-cluding diffusion/dispersion, convection and reaction phe-nomena, is presented.

Jolanta LewandowskaUniversity Montpellier 2Laboratory LMGCJolanta.Lewandowska@univ-montp2.fr

MS83

Modelling and Simulation of Chemical DegradationMechanisms in Porous Media with Evolving Mi-crostructure

A prototypical reaction–diffusion system in a porous

GS11 Abstracts 133

medium is considered, whose microstructure undergoes anevolution with respect to time. Employing the method ofhomogenization in domains with evolving microstructure,the limit problems are obtained. Attention is also paid tothe scaling of the material parameters with powers of thehomogenization parameter arising from a nondimensional-ization. For one class of applications, an efficient adaptivefinite element approach for the resulting limit problem ispresented.

Malte PeterInstitute of MathematicsUniversity of Augsburgmalte.peter@math.uni-augsburg.de

MS83

Homogenization of Biot-type Multi-compartementMedium with Double Porosity for Multiscale Mod-eling of Diffusion-deformation Processes

In the paper we report on homogenization of the dou-ble porous fluid-saturated deforming medium which is de-scribed by the Biot model. Both compressible and incom-pressible cases were considered. It is shown, how the topol-ogy of microstructure defined w.r.t. the dual porosity influ-ences structure of the homogenized model. Fading memoryeffects are explained in terms of flow in the dual porosity.Also large-deforming media were subject of homogeniza-tion applied to the updated Lagrangian formulation. Forlayered porous media with transversally periodic structure,the homogenization leads to models with reduced dimen-sion: ”3D to N times 2D”. The models are developed forsimulations of compact bone poroelasticity, or tissue peru-sion. Numerical examples are computed using our in-houseFEM code Sfepy.

Eduard RohanDept. of Mathematics, Faculty of Applied SciencesUniversity of West Bohemiarohan@kme.zcu.cz

Robert Cimrman, Vladimir LukesUniversity of West Bohemia, Pilsencimrman3@ntc.zcu.cz, lukes@kme.zcu.cz

MS84

Equations with Random Coefficients: Convergenceto Deterministic or Stochastic Limits and Theoryof Correctors

Equations with small scale structures abound in appliedsciences. Such structures often cannot be modeled at themicroscopic level and thus require that one understandtheir macroscopic influence. I will consider the situationof partial differential equations with random, highly oscil-latory, potentials. One is then interested in the behavior ofthe solutions to that equation as the frequency of oscilla-tions in the micro-structure tends to infinity. Depending onspatial dimension and the decorrelation properties of therandom potential, I will show that the limit is the solutionto either a deterministic, homogenized (effective medium)equation or a stochastic equation with multiplicative noise.More precisely, there is a critical spatial dimension abovewhich we observe convergence to a deterministic solutionand below which we observe convergence to a stochasticsolution. In the former case, a theory of correctors to ho-mogenization allows one to asymptotically capture the ran-domness in the solution to the equation with the small scalestructure. Once properly rescaled, this corrector is shown

to solve a stochastic equation with additive noise.

Guillaume BalColumbia UniversityDepartment of Applied Physics and Applied Mathematicsgb2030@columbia.edu

MS84

Error Estimates on Homogenization of Free Bound-ary Velocities

I will talk about a free boundary problem which describescontact angle dynamics on an inhomogeneous surface. Weobtain an estimate on the convergence rate of the freeboundaries to the homogenization limit in periodic media.The method presented here also applies to more generalclasses of free boundary problems with oscillating bound-ary velocities.

Inwon KimDepartment of MathematicsUCLAikim@math.ucla.edu

MS84

Multi-scale Analysis for Problems Where ClassicalHomogenization Fails

It is known that in many real situations, the classical ho-mogenization theory fails to provide a robust and reliablemacroscale approximation model for the given microstruc-ture. In this talk I will discuss about possible alternativeideas to deal with such situations.

Daniel OnofreiDepartment of MathematicsUniversity of Utahonofrei@math.utah.edu

Bacim AlaliMathematics DepartmentUniversity of Utahalali@math.utah.edu

MS84

Corrector Estimates for a Reaction-diffusion Sys-tem Modeling Sulfate Corrosion

A semi-linear partially-dissipative reaction-diffusion sys-tem modeling concrete corrosion in sewer pipes is consid-ered. The microstructure contains three non-overlappingregions: the solid matrix, the pore water clinging on solidfabrics and the air-filled part of the pore. A particular fea-ture of the microscopic model is that two interface-reactionmechanisms, the Henry’s law and a nonlinear chemical re-action on the boundary of pore walls, are balanced by thediffusive transport. The quality of the averaging procedureis defined by means of error estimates. We construct firstorder correctors and derive error estimates using the un-folding method, which enables the proof of error estimateswithout additional regularity of the correctors.

Mariya PtashnykDepartment of Mathematics IRWTH Aachen Universityptashnyk@math1.rwth-aachen.de

Adrian Muntean

134 GS11 Abstracts

Department of Mathematics and Computer ScienceTU Eindhovena.muntean@tue.nl

Tasnim FatimaDepartment of Mathematics and Computer ScienceTU Eindhoven, NLt.fatima@tue.nl

MS85

Robust Convex Optimization for Closed LoopReservoir Management

Abstract not available at time of publication.

Remus G. HaneaTNO Built and Environment,remus.hanea@tno.nl

MS85

Integrated Dynamic Optimization and Control inReservoir Engineering

Abstract not available at time of publication.

Jan Dirk JansenTechnische Universiteit DelftShell International E&Pj.d.jansen@tudelft.nl

MS85

Hierarchical Long-term and Short-term Produc-tion Optimization

Abstract not available at time of publication.

Gijs van EssenDelft University of Technologyg.m.vanessen@tudelft.nl

PP1

Iterative Solution of Non-Autonomous Bloch Equa-tions: Fluorescence Spectrum with DetunedSqueezed Vacuum Field

The non-autonomous Bloch equations modelling a driven2-level atom in the presence of an off-resonant broadbandsqueezed vacuum (SV) field is treated analytically. Thisconcerns iterative solutions valid for large SV detuning pa-rameter but for arbitrary strength of the laser field. Com-putational results are presented for the averaged atomicvariables for various data and compared with the resonantSV field case. The iterated analytical results for nonzeroSV detuning are compared with the (exact) numerical so-lutions of the Bloch equations, hence we have an insightabout the range of other system parameters (other than theRabi frequency) for which the iterated solutions are validto O(10-2) or less. The main purpose of deriving theseanalytical results is to calculate analytically the transientfluorescent spectrum. For an initially ground-state atom,both the SV phase and detuning parameters induce pro-nounced asymmetrical spectrum in the strong field case.

Rania A. AlharbiKing abdullaziz university, mathematics department,KSAPo. Box 42696 Jeddah 21551rania.math@gmail.com

PP1

On the Development of An Adaptive TriangularDiscontinuous Galerkin Shallow Water Model

The precise simulation of geophysical phenomena is essen-tial for the development of hazard warning systems. There-fore, we develop an adaptive two-dimensional shallow wa-ter model based on the Discontinuous Galerkin method.For spatial discretization we utilize high-order nodal basisfunctions as øfirst introduced by Giraldo et. al in 2002 andthe underlying triangular mesh is generated with amatos(see Behrens et. al, 2005). We show fiørst results obtainedfrom running several testcases.

Nicole Beisiegel, Joern BehrensKlimaCampus, University of Hamburgnicole.beisiegel@zmaw.de, joern.behrens@zmaw.de

PP1

Pseudo-Steady State Attractors for Fully TransientForchheimer Flows in Porous Media

This work is focused on the dynamics of the generalizedForchheimer flows for slightly compressible fluids in porousmedia with given total flux on the boundary. The class ofthe flows which are time invariant to certain character-istics is introduced and explored. We proved that eachof the time invariant flow attracts fully transient flows forparticular boundary conditions independently to the initialdata. Some applied engineering aspects of the frameworkare considered.

Lidia BloshanskayaTexas Tech UniversityDepartment of Mathematics and Statisticslidia.bloshanskaya@ttu.edu

PP1

Developing Empirically Based Seismic Event Loca-tion Ground Truth Criteria for Regional SeismicNetwork in Ethiopia and Tibet

The International nuclear monitoring community relieson selection criteria for classifying seismic events at theGround Truth 5km level, which specifies the absolute lo-cation to within 5km. Regional-network locations can-not be validated using existing criteria. Using the resam-pling methodologies developed by Bondr et al. (2004) and(Boomer et al., 2010), we have obtained empirical criteriabased on measures of uniformity of azimuth and distancecoverage. Criteria are being developed for Ethiopia andTibet.

Richard A. BrazierThe Pennsylvania State University Dubois CampusCommonwealth College (Math Division)rab27@psu.edu

Kb BoomerBucknell Universitykb.boomer@bucknell.edu

PP1

Reduced Order Models for Uncertainty Quantifica-tion and Parameter Estimation in Subsurface Flows

Modern reservoir simulations with millions of degrees offreedom can be extremely costly to evaluate given a set

GS11 Abstracts 135

of input parameters representing boundary/initial condi-tions and flow field properties. Thus, studies that requiremany model evaluations at varying input parameters suchas sensitivity analysis, uncertainty propagation, or historymatching can be prohibitively expensive. Cheaper reducedorder models are necessary for such analyses. We proposea method for reduced order modeling of nonlinear dynam-ical systems. The model reduction method is comparableto reduced basis methods and POD-based model reduc-tion, where the reduced model is a linear combination ofa small set of model runs. The coefficients of the linearcombination are computed with a nonlinear least squaresmethod, and the minimized residual is used as an a pos-teriori error estimate on the reduced model. This errorestimate can also be used to find points in the parameterspace whose solution will maximally enhance the reducedbasis, i.e. as a guide for how to choose the parametersto run the full model. We consider as our model prob-lem a one-dimensional two-phase, three-component com-positional displacement. The parameters in our study arethe component K-values, i.e., ratio of the each componentsphase composition; for simplicity we use a constant K-valuemodel. The predicted recovery from a reservoir is depen-dent on the solution path which in turn has a highly non-linear dependence on the K-values (even when these aretaken to be constants). As a proof of concept, we use thereduced order model as a surrogate in a maximum entropyinversion method to find the K-values that are consistentwith a given production history.

Paul ConstantineSandia National Labspconsta@sandia.gov

Jeremy E. KozdonStanford UniversityGeophysicsjkozdon@stanford.edu

Margot GerritsenDept of Petroleum EngineeringStanford Universitymargot.gerritsen@stanford.edu

PP1

Sensitivity of Co2 Storage Formation Pressuriza-tion and Migration to Uncertainty in Fault Zonesand Reservoir Properties: a Case Study.

We investigate here the potential impact of geologic carbonsequestration in a partially compartmentalized sandstonebasin in the Southern San Joaquin Valley in California,USA. Uncertainty about fault behavior is addressed by as-sessing four distinctive fault property scenarios. A sys-tematic sensitivity study is conducted for each scenario toidentify near- and far-field key hydrogeological parametersand processes affecting pressure buildup and brine migra-tion.

Andrea CortisEarth Sciences Division, 90-1116Lawrence Berkeley National Laboratoryacortis@lbl.gov

Jens T. BirkholzerLawrence Berkeley National Laboratory(LBNL)JTBirkholzer@lbl.gov

Stefan FinsterleLawrence Berkeley National Laboratory (LBNL),BerkeleyHydrogeology & Reservoir Dynamics DepartmentSAFinsterle@lbl.gov

Quanlin ZhouLawrence Berkeley National Laboratory (LBNL)qzhou@lbl.gov

PP1

Flow of Compressible Fluids Through Cracks inElastic Bodies and Excitation of Seismic Waves inVolcanic Eruptions

We investigate the eruption of fluids through conduits inelastic bodies, with particular focus on the excitation ofseismic waves by conduit wall oscillations induced by fluidflow. The fluid, an isothermal mixture of exsolved gas andliquid melt, obeys quasi-one-dimensional mass and momen-tum balance equations and a nonlinear equation of statedescribing compressibility changes during gas exsolution.Both the elastic wave equation and the fluid equations aresolved with high order finite differences.

Eric M. Dunham, Darcy OgdenDepartment of GeophysicsStanford Universityedunham@stanford.edu, deogden@stanford.edu

PP1

A Fully Implicit Solution Method Capability in theSpectral Element Community Atmosphere Model

Grid refinement of the Community Atmopshere Model(CAM) creates new algorithmic challenges including cou-pled nonlinear dynamics, physics, and chemistry, multipledisparate time scales, and scalability requirements. In ad-dition, new capabilities to analyze model sensitivities aredesired. Solution methods that address these issues arebecoming increasingly important. A fully implicit (FI) so-lution method is applied to the shallow water and primi-tive equations within the spectral element dynamical core(CAM-HOMME) and early results are presented. FI pro-vides a coherent nonlinear solution to all dependent vari-ables and allows relatively large time steps to be taken sta-bly without subcycling and with demonstrated accuracy.The solver implementation is occurring through the de-velopment of a Fortran interface package for the Trilinosproject that has been applied to several components of theCommunity Earth System Model.

Katherine J. EvansOak Ridge National Laboratoryevanskj@ornl.gov

PP1

Simulation of Supercritical Carbon Dioxide Seep-age from An Injection Well

We present a numerical model that simulates flow andtransport of CO2 into a multi-layered subsurface system.The model uses state-of-the-art multi-threaded finite ele-ment methods and unstructured adaptive mesh refinementscheme. Several scenarios spanning from a homogeneoussingle layered reservoir to heterogeneous multi-layered sys-tems, which including cap-rock with embedded fractures,have been simulated under different operations of CO2

136 GS11 Abstracts

leaking conditions. Results show the impact of leakagerates impact on the evolution of the CO2 spread.

Souheil M. Ezzedine, Ilya Lomov, Lee Glascoe, TarabayAntounLLNLezzedine1@llnl.gov, lomov1@llnl.gov, glascoe1@llnl.gov,antoun1@llnl.gov

PP1

Simulation and Upscaling of Nonaqueous PhaseLiquid Dissolution in Three Dimensional SaturatedPorous Media

We present an integrated experimental and computationalapproach aimed at quantitatively investigating the role ofpore structure, entrapped DNAPL distribution and hydro-dynamic conditions on core-scale mass transfer rates. Anumerical model was developed using adaptive mesh re-finement finite elements method. The numerical modelsolves simultaneously Navier-Stokes flow and transportwith state-of-the art embedded interface tracking scheme.The model was used to derive upscaled mass transfer ratesfor different soil types.

Souheil M. EzzedineLLNLezzedine1@llnl.gov

Russell DetwilerUC Irvineezzedine1@llnl.gov

Walter McNabLawrence Livermore National Labmcnab1@llnl.gov

Lee GlascoeLLNLglascoe1@llnl.gov

PP1

Application of Fractal Geometry in Evaluation ofPlagioclase Mineralization: Case Study IgneousRocks in Moshiran Area, Nw Iran

The area under study is situated in North-west of Iran.This area contains volcanic rock sequences from Basalticto Andesitic composition related to volcanic processes inEocene. Plagioclase were analyzed by statistical methodsto test for fractal behavior. The analysis shows that self-affine fractal geometry can be used to characterize the zon-ing patterns of this minerals. Generally low abundance ofsmall plagioclase crystals increases to 5-15% with some aslarge as 12 mm long. The crystal size distributions of thesecrystals mostly plot as almost straight lines on a classicCSD diagram. fractal dimension of Plagioclase crystals inthis area have calculated using fractal geometric methodssuch as box-counting. we can from this studies results con-clude that factors operating on scales much larger than thelocal interface processes are most important in controllingthe zonation.

Mohammad FadaeyanPayame Noor University Of Ardebilm fadaeyan@pnu.ac.ir

PP1

Application of Fractal Geometry in Evaluation ofPlagioclase Mineralization: Case Study IgneousRocks in Moshiran Area, Nw Iran

It is widely accepted that many of Minerals show scale in-variance, i.e. they are self-similar within a large range ofscales. In this paper, fractal dimension of Plagioclase crys-tals in Basaltic, Andesitic rocks from Moshiran area in NWof Iran have calculated using box-counting method. Im-age analysis techniques are applied and fractal dimensionvaries between 1.5 to 1.85 that correspond with geochem-ical modeling of magma mixing Coupled fractal analysisand geochemical data reveal that D increases as the de-gree of magma interaction and show that homogenizationpaterns increases in magma. An other hand this studyindicated that present of zoning structures in Plagioclasecrystals have relation between fractal geometry functions.fractal geometry can help to interpretation of varies kindtexture in rocks.

Mohammad FadaeyanPayame Noor University Of Ardebilm fadaeyan@pnu.ac.ir

PP1

An Alternative Splitting for Two-Phase Flow withCapillary Pressure

A subset of problems in two-phase groundwater flow fea-ture diffusive capillary pressure terms that balance the ad-vective motion of the fluid. One numerical method de-signed to solve these advection-diffusion PDEs is a splitmethod where the advective and diffusive parts are solvedseparately. This works well when either advection or dif-fusion dominates; however, when these terms are supposedto balance, this splitting can lead to a severe time-step re-striction. We propose a variation of this method that pre-serves the balance between the two effects while enabling alarger time-step that is based on an f-wave decompositionof the flux. We show results from this formulation for agroundwater flow problem.

Kirsten M. FagnanLawrence Berkeley National Laboratorykmfagnan@lbl.gov

George PauLBNLGPau@lbl.gov

John B. BellLawrence Berkeley National Laboratoryjbbell@lbl.gov

PP1

Direct Simulations of Dynamic Interfaces in Com-plex Geometry

Multiphase flow in porous media is dictated by the be-havior of fluid-fluid interfaces, which affects phase distri-bution through hysteresis and instability. To investigatethese phenomena, we perform direct numerical simulationsof a 2D two-phase system. The full Navier-Stokes equa-tions are solved in the pore space and the Volume of Fluidmethod is used to track the interfaces. Particular atten-tion is paid to interfacial energy and to the effects of the

GS11 Abstracts 137

velocity on phase distribution.

Andrea Ferrari, Riccardo ManieroInstitute of GeophysicsUniversity of Lausanneandrea.ferrari@unil.ch, riccardo.maniero@unil.ch

Ivan LunatiUniversity of Lausanneivan.lunati@unil.ch

PP1

Comparison of Preconditioning Techniques for Op-timizing a Nonhydrostatic, Parallel Tsunami Sim-ulation Model

The Tsunami Modelling Group at Alfred-Wegener-Institute has developed a tsunami simulation tool with aP1 − P NC

1 Finite Element discretization on unstructuredgrids and a Leapfrog time-stepping scheme. For higheraccuracy a set of equations similar to the shallow waterequations has to be solved. The major percentage of theresources is required by the computation of several large,sparse systems of equations. By comparison of miscella-neous preconditioning techniques their individual capabil-ities of optimization are presented.

Annika FuchsAlfred-Wegener-Institute for Polar and Marineannika.fuchs@awi.de

Stephan Frickenhaus, Wolfgang Hiller, Rakowsky NataljaAlfred-Wegener-Institute for Polar andMarine Researchstephan.frickenhaus@awi.de, wolfgang.hiller@awi.de, na-talja.rakowsky@awi.de

PP1

Synthetic 3D Simulations from Real Models withTopography

I show finite-difference discretizations of (visco-)elasticwave equations including free surface topography bound-ary conditions, using an exact transform from a verticallycurved (stretched) grid to a rectangular (computational)grid. I simulate real areas of 3D models covered by to-pography. Qualitative effects are shown of prominent freesurface topography on wavefields, comparing and isolat-ing effects of using real and homogeneous interior media,as well as assessing effects of adding viscoelasticity to theresults.

Stig O. HestholmExxonMobil Upstream Research CompanyStig.Hestholm@exxonmobil.com

PP1

A-Priori Estimates for Non-Equilibrium Systems

We discuss extensions and applications of a-posteriori anal-ysis for a coupled linear system of PDEs known in multi-scale analysis as Warren-Root model. Its structure extendsreadily to nonlinear models of non-equilibrium adsorption,Enhanced CoalBed Methane Recovery, and other kineticmodels. In this poster we show numerical results for thea-posteriori analysis and for the applications.

Viviane Klein

Oregon State Universitykleinv@math.oregonstate.edu

Malgorzata PeszynskaDepartment of MathematicsOregon State Universitympesz@math.oregonstate.edu

PP1

Vertical Equilibrium Simulation with 3D Near-WellModeling

Lack of vertical resolution may cause 3D simulations ofCO2 sequestration to be inaccurate. To increase accuracyand reduce computational cost, a thin CO2 plume can beapproximated in terms of its thickness to obtain a 2D sim-ulation model. However, the corresponding assumption ofvertical equilibrium is not fulfilled near an injecting well.Herein, we therefore develop a method in which a verti-cal equilibrium formulation is coupled with a standard 3Ddiscretization near the well.

Ingeborg Ligaarden, Halvor NilsenSINTEFingeborg.ligaarden@sintef.no, halvormoll.nilsen@sintef.no

PP1

Mimetic Finite Difference Methods for ModelingSubsurface Flows

Mimetic finite difference (MFD) methods mimic importantproperties of underlying PDEs, such as conservation laws,symmetry and positivity of a solution, and fundamentalidentities of the vector and tensor calculus. This posterwill summarize our progress in development and analysisof MFD methods as well as they usage in applied projectsfor modeling subsurface flows on distorted unstructuredpolyhedral grids.

Konstantin LipnikovLos Alamos National Laboratorylipnikov@lanl.gov

PP1

Seismic Processing of Diffractions

A main task in seismic data interpretation is the identifica-tion of sharpened objects in the subsurface, such as faultsor channels. When these structures are small enough, theydiffract the energy emitted by the acquisition process. Wepropose a method that optimize the traditional seismic pro-cessing, by considering the diffractions as information in-stead of noise, to locate points at the velocity model wherediffractions are made, and thus generating better imagesof the subsurface.

Susanne R. MacielUniversidade de Brasiliasusanne@unb.br

Ricardo BilotiUniversidade Estadual de Campinasbiloti@ime.unicamp.br

PP1

Reducing Hurricane Storm Surge Model Error Us-

138 GS11 Abstracts

ing the Ensemble Kalman Filter

Error is inherent in every dynamical model and in observa-tions of the model solution. Given both, data assimilationmethods are used to compute the best estimate of state.The Ensemble Kalman Filter is an advanced data assim-ilation method for nonlinear problems. Here it is appliedto the Advanced Circulation (ADCIRC) model to betterpredict hurricane storm surge using water elevation mea-surements.

Talea L. MayoThe University of Texas at Austintalea.mayo@gmail.com.

PP1

Tectonic Evolution at Rift Zones: Geodynamicsand Numerical Modeling

Tectonic evolution at rift zones is commonly consideredsymmetric along mid-ocean ridges, when modeling withrelative plate motions and steady-state processes. How-ever, the bathymetry of rift zones is generally asymmet-ric. Adopting an absolute frame of reference, we performedsimulations using FEM: the mantle is modeled as a viscousnon-newtonian fluid, and its dynamics is described by theStokes equations. Results show an asymmetric thickeningof plates along the ridge, as suggested by the observations.

Marco CuffaroIstituto di Geologia Ambientale e GeoingegneriaCNRmarco.cuffaro@uniroma1.it

Carlo DoglioniUniversita La Sapienzacarlo.doglioni@uniroma1.it

Edie Miglio

Politecnico di Milano (Italy)MOX, Dept. of Mathematicsedie.miglio@polimi.it

PP1

A New Adaptive Multiscale Fem Applied to Inter-face Problems

We introduce a new adaptive multiscale finite elementmethod (AMsFEM) that greatly improves convergencewhilst still being conforming. AMsFEM is an extension ofthe adaptive local-global multiscale finite element methodby Durlofsky et al. The idea is to keep the mesh fixedand instead iteratively adapt the shape of the basis func-tions in the approximation space. This allows fine scaledata to be incorporated in to local problems for the ba-sis functions whilst still having a coarse global system tosolve. We present applications of this to structural opti-mization problems but they can be applied to groundwaterflow problems also.

Ray MillwardDept of Mathematical SciencesUniversity of Bathr.r.millward@bath.ac.uk

PP1

Coupled High-Order Finite Difference and Un-

structured Finite Volume Methods for EarthquakeRupture Dynamics in Complex Geometries

Spontaneous rupture models are becoming increasinglyused to study scenario earthquakes and to assess seis-mic hazard. High-order numerical methods are ideallysuited for these problems, but stable, accurate, and effi-cient methods are needed to incorporate the nonlinear fric-tion laws. We present our latest developments on the useof summation-by-parts finite difference methods and thesimultaneous approximation term method for such prob-lems, with a focus on using unstructured grids.

Ossian OreillyDepartment of scientific computinguppsalaossian.oreilly@gmail.com

Jeremy E. KozdonStanford UniversityGeophysicsjkozdon@stanford.edu

Eric M. DunhamDepartment of GeophysicsStanford Universityedunham@stanford.edu

Jan NordstromMathematicsLinkoping Universityjan.nordstrom@liu.se

PP1

Porescale Benchmark: Call for Participation

[Organizers; M. Peszynska, Dorthe Wildenschild, OregonState University]. We propose to define a set of bench-marks in porescale modeling organized by a group of re-searchers involved in the computational and experimentalmodeling at porescale. We define the goals, propose theonline venue, and outline the directions, applications, tech-niques, as well as timeline. In particular, we include singleand multiphase flow, biofilms and reactive transport mod-eling, and a variety of techniques including continuum todiscrete computations. This poster is intended as a call forparticipation in this benchmark.

Malgorzata PeszynskaDepartment of MathematicsOregon State Universitympesz@math.oregonstate.edu

PP1

Testing Nonhydrostatic Sound-Proof Equations AsProspective Governing Pde for Regional WeatherPrediction

The nonhydrostatic anelastic model EULAG, for researchof multiscale atmospheric flows, is considered as a prospec-tive dynamical core of a future operational regional nu-merical weather prediction (NWP) model of the EuropeanCOnsortium for Small scale Modeling (COSMO), antici-pated to operate at kilometer- and sub-kilometer horizontalresolutions. Results of dry and moist idealized and semi-idealized tests are summarized and supplemented with ex-amples of realistic sub-kilometer NWP-like simulations of

GS11 Abstracts 139

the Alpine flows.

Zbigniew P. PiotrowskiNational Center for Atmospheric Researchpiotrows@ucar.edu

Marcin Kurowski, Bogdan RosaInstitute of Meteorology and Water Managementmarcin.kurowski@imgw.pl, bogdan.rosa@imgw.pl

Andrzej WyszogrodzkiNCARMMMandii@ucar.edu

Michal ZiemianskiInstitute of Meteorology and Water Managementmichal.ziemianski@igmw.pl

PP1

The Impact of Single-Phase Upscaling on Polymer-Flooded Reservoirs

Upscaling of geological data to reservoir models is com-mon practice in reservoir simulation. However, reducingthe number of grid blocks introduces errors in the simula-tion due to computational discretization and loss of reser-voir heterogeneity. Typically upscaling studies focus onNewtonian fluid injection, e.g. water flooding, whereas theeffects of upscaling on non-Newtonian fluid flow behaviorare not well understood. In this study, we examine theeffect of upscaling polymer-floodings.

Potcharaporn Pongthunya, Peter KingImperial College Londonp.pongthunya08@imperial.ac.uk,peter.king@imperial.ac.uk

PP1

An Alternative to Streamlines for Flow Diagnosticson Structured and Unstructured Grids

In this paper, we investigate finite volume methods as analternative to traditional streamline-based methods for ob-taining flow diagnostic information. Given a computed fluxfield, we solve the stationary transport equations for tracerand time of flight on a fixed grid to partition the reservoirinto injector-producer pairs and to assess the heterogene-ity of the reservoir. We show that a multi-dimensionalupstream weighting scheme is able to reduce the numericaldiffusion associated with the method.

Mohammad ShahvaliStanford Universityshahvali@stanford.edu

Bradley MallisonChevron Energy Tech. Cobtmb@chevron.com

Herve GrossChevron Energy Technology Companyhgross@chevron.com

PP1

Energy Bounds for the Equations of Mantle Dy-

namics

We present energy estimates for the partial differentialequations of mantle dynamics, in a somewhat simplifiedform. We show that the fluid pressure blows up as themelt is lost. Therefore the fluid pressure variable cannotbe approximated in any simple way in a finite element andother approximation method.

Abraham L. TaicherUniversity of Texas at Austinataicher@ices.utexas.edu

Todd ArbogastDept of Math; C1200University of Texas, Austinarbogast@ices.utexas.edu

Marc A. HesseUniversity of TexasDepartment of Geological Sciencesmhesse@jsg.utexas.edu

PP1

Coupling of the Evolution of Pore Pressure and theRetrogressive Slope Failure During Breaching

Breaching is a type of slope failure that, due to the porepressure response, produces retrogressive sediment release.We study the connection between the pore pressure dis-sipation and the retrogressive slope failure through flumeexperiments and numerical modeling. We find the erosionrate of breaching is proportional to the coefficient of con-solidation, and the spatial distribution of pore pressure isself-similar through time.

Yao YouJackson School of GeosciencesThe University of Texas at Austinyaoyou@mail.utexas.edu

Peter B. FlemingsThe University of Texas at AustinJackson School of Geosciencespflemings@jsg.utexas.edu

David MohrigJackson School of GeosciencesThe University of Texas at Austinmohrig@jsg.utexas.edu

PP1

Model of Mineralization of Rainwater PassingThrough a Rock

Geochemical interactions of rainwater passing through arock was modelled. The main chemical components andthe governing equlibrium and kinetic chemical reactionswere identified. Sensitivity analysis of some parametersof the model was done to better understand the model.The model was used to inverse modelling - calibration ofseveral parameters of a real-world problem - using mea-surement data published before. Acknowledgement: Thisresult was realized under the state subsidy of the CzechRepublic within the project No. 1M0554

Ivan BruskyInstitute of Novel Technologies and Applied InformaticsTechnical University of Liberec

140 GS11 Abstracts

ivan.brusky@tul.cz

Jan SemberaThe Institute of Novel Technologies and AppliedInformaticsTechnical University of Liberecjan.sembera@tul.cz

PP1

Calibration of Rainfall-Runoff Hydrological Modeland Flood Simulation Using Data Assimilation

This work focuses on the calibration of a distributed par-simonious event-based rainfall-runoff model using data as-similation. In the present work, a BLUE filtering techniquewas used to calibrate the initial water deficit and the veloc-ity travel for each flood event assimilating the first avail-able discharge measurements at the catchment outlet. Theassimilation algorithm was applied on two Mediterraneancatchment areas of different size and dynamics: Gardond’Anduze and Lez. On both catchments, it was shown overa significant number of flood events, that the data assim-ilation procedure improves the flood peak forecast. Theimprovement is globally more important for the Gardond’Anduze catchment where the flood events are stronger.The peak can be forecasted up to 36 hours head of timefor some events. Such results are obtained assimilatingvery few observations (up to 4) during the rise of the wa-ter level. For multiple peaks events, the assimilation ofthe observations from the first peak leads to a significantimprovement of the second peak simulation. It was alsoshown that the flood rise is often faster in reality than it isrepresented by the model. In this case and when the floodpeak is under estimated in the simulation, the use of thefirst observations can be misleading for the data assimila-tion algorithm. The careful estimation of the observationand background error variances enabled the satisfying useof the data assimilation in these complex cases even thoughit does not allow the model error correction.

Sophie ricci, Sophie ricciCERFACSricci@cerfacs.fr, ricci@cerfacs.fr

andrea piacentini, Olivier ThualCerfacspiacentini@cerfacs.fr, thual@cerfacs.fr

mathieu coustauHSMcoustau@msem.univ-montp2.fr