Modeling Emerging Modeling Emerging Magnetic FluxMagnetic Flux

W.P. Abbett, G.H. Fisher W.P. Abbett, G.H. Fisher

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Y. FanY. Fan

Sub-surface ModelingSub-surface Modeling

ANMHD --- 3D MHD in the anelastic ANMHD --- 3D MHD in the anelastic approximationapproximation

Pseudo-spectral techniquePseudo-spectral technique Code is mature --- optimized for use on Code is mature --- optimized for use on

both shared and distributed memory both shared and distributed memory machines (eg. IBM SP, SGI Origin 3800), machines (eg. IBM SP, SGI Origin 3800), as well as single-processor workstationsas well as single-processor workstations

Numerical algorithm allows for extensiveNumerical algorithm allows for extensive exploration of parameter space exploration of parameter space

ANMHD Examples: LHS --- magneto-convection and the local solar dynamo;RHS --- emerging magnetic flux.

Of interest: Highly twisted, knotted configurations (Linton, Fan, Fisher)

Kink unstable magnetic flux tube rising through a stratified model CZ (LHS using ANMHD -- Fanet al.) and evolving in a non-stratified domain using a periodic spectral code (RHS -- Linton).

Delta Spot Active Regions modeled as Delta Spot Active Regions modeled as buoyant, initially kink-unstable flux tubes buoyant, initially kink-unstable flux tubes that emerge through CZ (Linton et al.)that emerge through CZ (Linton et al.)

Q: Is emerging flux (especially in highly sheared configurations)an important component of the CME initiation process?

ANMHD --- SummaryANMHD --- Summary

Provides numerous, simulated active Provides numerous, simulated active region datasets that can be used to region datasets that can be used to provide provide self-consistentself-consistent, depth dependent , depth dependent sub-photospheric velocity and magnetic sub-photospheric velocity and magnetic fields for input into global coronal modelsfields for input into global coronal models

Future development plans: SANMHD (3D Future development plans: SANMHD (3D spherical ANMHD --- Bercik)spherical ANMHD --- Bercik)

Modeling the CoronaModeling the Corona

PARAMESHPARAMESH: A domain decomposition, : A domain decomposition, adaptive mesh refinement (AMR) framework adaptive mesh refinement (AMR) framework developed by MacNeice et al. and distributed by developed by MacNeice et al. and distributed by GSFCGSFC

Zeus3DZeus3D: A staggered mesh finite-difference : A staggered mesh finite-difference (non-relativistic) MHD code originally developed (non-relativistic) MHD code originally developed by Stone, Norman, and Clarke and publicly by Stone, Norman, and Clarke and publicly distributed by NCSAdistributed by NCSA

ZeusAMRZeusAMR: A fully compressible 3D MHD code : A fully compressible 3D MHD code with AMR which resulted from a merge of with AMR which resulted from a merge of PARAMESH with a modified version of Zeus3DPARAMESH with a modified version of Zeus3D

Local Zeus3D(no AMR) flux emergence calculation

Example of driving a ZeusAMR coronalsimulation with an ANMHD generated lowerboundary. True “code coupling” can be achieved using the PARAMESH framework.

ZeusAMR Progress: Tasks CompletedZeusAMR Progress: Tasks Completed Merged Zeus3D with PARAMESH v2.x (decomposition Merged Zeus3D with PARAMESH v2.x (decomposition

technique optimized for SGI shared memory technique optimized for SGI shared memory architectures)architectures)

ZeusAMR transport step no longer directionally split ZeusAMR transport step no longer directionally split (Fan)(Fan)

ZeusAMR written to enhance portability: the NCSA ZeusAMR written to enhance portability: the NCSA editor and input decks are eliminated in favor of more editor and input decks are eliminated in favor of more modern, portable preprocessors and I/0.modern, portable preprocessors and I/0.

Incorporated boundary conditions and refinement criteria Incorporated boundary conditions and refinement criteria appropriate for simulating flux emergence into the low appropriate for simulating flux emergence into the low coronacorona

Added option to include the “Boris Correction” Added option to include the “Boris Correction”

Incorporated an approximate treatment of transition Incorporated an approximate treatment of transition region heating and cooling termsregion heating and cooling terms

ZeusAMR: Tasks Nearly CompleteZeusAMR: Tasks Nearly Complete

Implement and test the polar and lower radial Implement and test the polar and lower radial boundary conditions when running 3D MHD boundary conditions when running 3D MHD simulations in spherical coordinatessimulations in spherical coordinates

Incorporate explicit resistivity into the codeIncorporate explicit resistivity into the code

Develop a user-friendly means of incorporating Develop a user-friendly means of incorporating an initial global coronal atmosphere into a pre-an initial global coronal atmosphere into a pre-defined, ZeusAMR block structuredefined, ZeusAMR block structure

ZeusAMR: Future developmentZeusAMR: Future development

Upgrade PARAMESH routines to v3.0 (more Upgrade PARAMESH routines to v3.0 (more efficient mpi treatment for distributed memory efficient mpi treatment for distributed memory architectures)architectures)

Add optically thin radiative cooling and Add optically thin radiative cooling and conduction along fieldlines to the equation of conduction along fieldlines to the equation of internal energyinternal energy

Incorporate the improved MoC algorithm, and Incorporate the improved MoC algorithm, and the two temperature treatment of Clarkethe two temperature treatment of Clarke

Summary:ANMHD can provide a varietyof simple (to more complicated)datasets to incorporate intothe boundaries of global (or local) simulations of the corona.

Different configurations canBe readily generated; the Images on the left wereCalculated on a 1.2GHzAthlon PC in ~8 hours