1. The CRASH code: test matrix Eric S. Myra CRASH University of Michigan October 19, 2009

2. 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

3. 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.

4. 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 RADIOGRAPHY FULL SYSTEM

5. 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 implemented implemented since last review in progress for next review Radiation Light-front propagation (FLD & S n ) Multi-group light front (FLD) Su-Olson Diverse (~ 80) S n 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

6. Page 6 Our verification suite is steadily expanding to provide better code coverage and test new functionality Hydro 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 implemented implemented since last review in 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

7. Page 7 The CRASH test matrix shows increasingly good code and feature coverage Each verification test has a quantitative pass/fail criterion.

8. Page 8 The CRASH test matrix shows increasingly good code and feature coverage Each verification test has a quantitative pass/fail criterion. Example: the Su-Olson problem tests pure diffusion.

9. 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: C v  T 3 –solved for two mixed explicit–implicit methods: E rad and E int 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.)

10. 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  1 st -order accuracy in time Lagged Knudsen number for FLD Cross-solver tests: performed for gray FLD, multigroup FLD, discrete-ordinates gray FLD  t = 0.05 t CFL-rad x (cm) E rad (erg cm -3 ) numerical solution analytic solution

11. Page 11 An infinite medium approaches radiative equilibrium No spatial transport System is allowed to equilibrate using only radiation–matter energy exchange Initially: T rad = 0; T mat = 1.32 keV Finally: T rad = T mat = 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.

12. 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, J 0 in r) –Crank-Nicolson used for both to achieve 2 nd -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 (T e = T i ) –thermal wave mimics radiative precursor in CRASH problem

13. 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 T ions (eV) x (cm) grid resolution T elec (eV) 1 st -order slope

14. Page 14 Modified Lowrie-3: evolution of temperatures ION TEMPERATURE ELECTRON TEMPERATURE AREA OF STATIC GRID REFINEMENT x y LOCATION OF ADVANCING FRONTS

15. Page 15 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 T b conduction dominates the fluid flow thermal front leads hydro shock self-similar analytic solution exists tested using r-z geometry 1 st -order slope relative error radius radial velocity temperature density

16. 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

17. 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