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The CRASH code: test matrix
Eric S. MyraCRASH
University of MichiganOctober 19, 2009
Page 2
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
Page 3
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.
Page 4
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
Page 5
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
Page 6
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
Page 7
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
Time-evolution scheme
Each verification test has a quantitative pass/fail criterion.
Page 8
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
Tested code components
Active variables
Verification test problems
Hydro scheme
Grid resolution
Radiation treatment
Diffusion term
Equation of stateHeat Conductivity
Time-evolution scheme
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.
Page 9
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.)
Page 10
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
Page 11
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.
Page 12
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
Page 13
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
Page 14
Modified Lowrie-3: evolution of temperatures
ION TEMPERATURE
ELECTRON TEMPERATUREAREA OF STATIC GRID REFINEMENT
x
y
LOCATION OF ADVANCING FRONTS
Page 15grid 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
Page 16
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
Page 17
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
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 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
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
Active variables
Tested code components
Verification test problems
Grid resolution
Radiation treatment
Diffusion term
Equation of stateHeat Conductivity
Time-evolution scheme
Hydro scheme