the crash code: test matrix eric s. myra crash university of michigan october 19, 2009

The CRASH code: test matrix

Eric S. MyraCRASH

University of MichiganOctober 19, 2009

This talk is a status update and part of our response to the review-team recommendations in the V&V area

Outline:

• Approach to testing

• Test coverage

• Test matrix

• Specifics of selected tests

Verification is motivated by several viewpoints

• Verification: The process by which one demonstrates that a … code correctly solves its governing equations.

– Knupp & Salari, 2003

• Equation: terms and sets of terms• Code component: subroutines and

functions• Functionality: code features• Experiential: unexpected behavior

Adding to, modifying, and using the code motivates the addition

of tests.

Multiple classes of tests are in our suite

• Hydrodynamics

• Radiation transport

• Radiation

hydrodynamics

• Heat conduction

• Simulated radiography

• Material properties

• EOS

• opacities

• Unit tests

• Full-system tests

HEAT CONDUCTION

RADIATION TRANSPORT

HYDRODYNAMICS

RADIATION HYDRODYNAMICS

SIMULATED RADIOGRAPHYFULL SYSTEM

Our verification suite is steadily expanding with new tests

Hydrodynamics• Sound-wave problem (ideal gas)• Shu-Osher (1D, 2D; ideal gas)• Multi-material advection • > 20 HD and MHD tests in BATSRUS

Heat conduction• Uniform conduction coefficient• Reinicke & Myer-ter-Vehn • Lowrie-3 for electrons

Simulated Radiography• Simple shapes; analytic

solutions• Shock-tube images in 2 and 3D

previously implementedimplemented since last reviewin progress for next review

Radiation• Light-front propagation (FLD &

Sn)

• Multi-group light front (FLD)• Su-Olson

• Diverse (~ 80) Sn neutronics

tests adapted for CRASH• Infinite medium• Diffusion of radiation pulses• Flux-divergence• Graziani radiating sphere

Radiation Hydrodynamics• Lowrie test problems (1, 2, & 3)

– mixed explicit–implicit • Mihalas acoustic wave damping by

radiation• McClarren MMS

Our verification suite is steadily expanding to provide better code coverage and test new functionalityHydro scheme• HLLE• Godunov

Radiation scheme• gray flux-limited diffusion• multigroup flux-limited

diffusion• discrete ordinates• coupled discrete ordinates

Heat Conduction• uniform conductivity• self consistent

Electron-Ion Coupling

Solvers and preconditioners

• conjugate gradient• GMRES• DILU/BILU preconditioners• new solvers and

preconditioners, as required

previously implementedimplemented since last reviewin progress for next review

Time-evolution scheme

• fully implicit• mixed explicit–

implicit

Grid Resolution• uniform• static AMR• dynamic AMR

Equation of State• polytropic• self consistent

Opacities• SESAME• self consistent

Dimensionality• Cartesian

1,2,3D• cylindrical 2D

I/O Tests

Coupling Tests• PDT to BATSRUS

The CRASH test matrix shows increasingly good code and feature coverage

Full System 1D Full System 2D Full System 3D Full system (nozzle) Full system (NIF) Infinite medium Light front Light front (double) Lowrie 1 (radiation) Lowrie 2 (radiation) Lowrie 3 (radiation) Lowrie 3 (mod; electrons) Multi-material advection Multi-material wave Radiography Reinicke Meyer-ter-Vehn Shu-Osher Sound wave Su-Olson Uniform heat conductionrho x x x x x x x x x x x x x x xmaterials x x x x x x xu x x x x x x x x x x x x x xE_int x x x x x x x x x x x x x x x x xE_rad x x x x x x x x x x x xgray diffusion x x x x x x x x x x xmultigroup diffusion x x x x x x x xdiscrete ordinates x x x x x x x x xpure diffusion x x x xflux-limited x x x x x x x xgamma law x x x x x x x x x x x x x x xself-consistent x x x x x x x xuniform/analytic x x xself-consistent x x x x x

Coupling electron-ion x x x x x xuniform/analytic x x x x x x xstd tabular x x x x x xself-consistent x x x x x xlevel-set x x x x x x xmixed cell x x x x x x x1D x x x x x x x x x x x2D x-y x x x x x x x x x x2D r-z x x x x x x x x x x3D x-y-z x x x x x x x x x x x x x xuniform x x x x x x x x x x x x x x x x x x xfixed AMR x x x x x x x x x x x x x x x x x x xdynamic AMR x x x x x x x x x x x x x x x x x xexplicit x x x ximplicit x x x x x x x x x x x x x x x x x x xmixed explicit-implicit x x x x x x x x x x x x xHLLE x x x x x x x x x x x x x xGodunov x x x x x x x x x x x x x xCG x x x x x x x x x x x x x x x x x x xGMRES x x x x x x x x x x x x x x x x x x x

Preconditioners DILU/BILU x x x x x x x x x x x x x x x x x x xHyades output x x x xuser specified x x x x x x x x x x x x x x x x

KEY Implemented test covers this physics/numerics/code component x Not presently implemented x

Test cannot cover this code component in a meaningful way

Implicit solvers

Initial conditions

Opacities

Multi-materials

Dimensionality

Tested code components

Active variables

Verification test problems

Hydro scheme

Grid resolution

Radiation treatment

Diffusion term

Equation of stateHeat Conductivity


Each verification test has a quantitative pass/fail criterion.

The CRASH test matrix shows increasingly good code and feature coverage


Coupling electron-ion x x x x x xuniform/analytic x x x x x x xstd tabular x x x x x xself-consistent x x x x x xlevel-set x x x x x x xmixed cell x x x x x x x1D x x x x x x x x x x x2D x-y x x x x x x x x x x2D r-z x x x x x x x x x x3D x-y-z x x x x x x x x x x x x x xuniform x x x x x x x x x x x x x x x x x x xfixed AMR x x x x x x x x x x x x x x x x x x xdynamic AMR x x x x x x x x x x x x x x x x x xexplicit x x x ximplicit x x x x x x x x x x x x x x x x x x xmixed explicit-implicit x x x x x x x x x x x x xHLLE x x x x x x x x x x x x x xGodunov x x x x x x x x x x x x x xCG x x x x x x x x x x x x x x x x x x xGMRES x x x x x x x x x x x x x x x x x x x





Active variables


Hydro scheme

Grid resolution

Radiation treatment

Diffusion term



Implicit solvers

Initial conditions

Opacities

Multi-materials

Dimensionality

Each verification test has a quantitative pass/fail criterion.

Example: the Su-Olson problem tests pure diffusion.

We have implemented new tests for radiation and rad-hydro

• Light front tests– fundamental test for any radiation solver—can we propagate

light?– serves as cross-solver coupling tests between matter and

radiation solvers (gray FLD, multigroup FLD, discrete ordinates, etc.)

• Su-Olson test– light-front test plus matter–radiation interaction– linearized problem: Cv T 3

– solved for two mixed explicit–implicit methods: Erad and Eint independently and together

• Lowrie radiation-hydrodynamics tests– updated to use mixed explicit–implicit solvers

• Infinite medium tests– test source-term implementation– also serve as coupling tests between matter solvers and

radiation solvers (gray FLD, multigroup FLD, discrete ordinates, etc.)

Light-front propagation in optically thin limit

• Behavior of the Boltzmann equation is hyperbolic.

• Challenge for flux-limited diffusion

• Test models the propagation of a radiation front, from inner edge of the domain to a point halfway into the domain.

• Timescale for this process is x/c

• In FLD solvers, we use backward Euler 1st-order accuracy in time

• Lagged Knudsen number for FLD

• Cross-solver tests: performed for gray FLD, multigroup FLD, discrete-ordinates

gray FLDt = 0.05 t CFL-rad

x (cm)

Erad (erg cm-3)

numerical solutionanalytic solution

An infinite medium approaches radiative equilibrium

• No spatial transport• System is allowed to equilibrate using only radiation–matter energy exchange

• Initially: Trad = 0; Tmat = 1.32 keV

• Finally: Trad = Tmat = 1 keV

• Shown for 2 groups below; 80 groups in the movie• Cross-solver tests: performed for gray FLD, multigroup FLD, discrete

ordinates

absolute error e-

folding time

time step (arbitrary units)

Our method gets the correct solution—at the

correct time.

We have implemented 3 new tests for electron heat conduction

• Uniform heat-conduction coefficient– 1D Gaussian temperature profile

– 2D r-z geometry (Gaussian in z, J0 in r)

– Crank-Nicolson used for both to achieve 2nd-order accuracy

• Modified Lowrie-3 test– example of test recycling.– rad-hydro test adapted for heat conduction.– diffusion applicable to both radiation and conduction– also tests electron–ion relaxation

• Reinicke & Meyer-ter-Vehn test– blast wave at origin expanding into ambient medium (Te =

Ti)

– thermal wave mimics radiative precursor in CRASH problem

Modified Lowrie-3 tests electron energy

• Recycled rad-hydro test with…– photons electrons– matter ions

• 2D non-uniform grid; variable opacities

• initial condition is rotated by arctan(0.5)

• solution is advected orthogonal to shock front

• a constant velocity added to steady state solution.

relative error

Tions (eV)

x (cm) x (cm)

grid resolution

Telec (eV)

1st-order slope

Modified Lowrie-3: evolution of temperatures

ION TEMPERATURE

ELECTRON TEMPERATUREAREA OF STATIC GRID REFINEMENT

x

y

LOCATION OF ADVANCING FRONTS

grid resolution

Reinicke & Meyer-ter-Vehn test gives us a “CRASH-like” problem

Analogous to Sedov-Taylor blast wave

• initial “bomb” at center

• heat conductivity a Tb

• conduction dominates the fluid flow

• thermal front leads hydro shock

• self-similar analytic solution exists

• tested using r-z geometry

1st-order slope

relative error

radius

radial velocity

temperature

density

Testing motivated by unexpected behavior:Shock protuberances

We are investigating sensitivity to• model dimensionality• EOS• opacity• axial symmetry

• initial conditions• radiation model• hydro solver flux

function

Verification is ingrained in the CRASH culture

• We have a rich set of tests.

• We have a process in place.

• We have good and improving coverage, including– analytic/semi-analytic problems

– unit tests – convergence studies – algorithmic comparisons – full system tests


Coupling electron-ion x x x x x xuniform/analytic x x x x x x xstd tabular x x x x x xself-consistent x x x x x xlevel-set x x x x x x xmixed cell x x x x x x x1D x x x x x x x x x x x2D x-y x x x x x x x x x x2D r-z x x x x x x x x x x3D x-y-z x x x x x x x x x x x x x xuniform x x x x x x x x x x x x x x x x x x xfixed AMR x x x x x x x x x x x x x x x x x x xdynamic AMR x x x x x x x x x x x x x x x x x xexplicit x x x ximplicit x x x x x x x x x x x x x x x x x x xmixed explicit-implicit x x x x x x x x x x x x xRusanov x x x x x x x x x x x x x xHLLE x x x x x x x x x x x x x xGodunov x x x x x x x x x x x x x xCG x x x x x x x x x x x x x x x x x x xGMRES x x x x x x x x x x x x x x x x x x x




Implicit solvers

Initial conditions

Opacities

Multi-materials

Dimensionality

Active variables



Grid resolution

Radiation treatment

Diffusion term



Hydro scheme

the crash code: test matrix eric s. myra crash university of michigan october 19, 2009

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