Code Comparison and Validation LA-UR Bruce Fryxell Center for Radiative Shock Hydrodynamics Fall 2011 Review

Code comparison collaboration includes researchers from three institutions CRASH – University of Michigan o Bruce Fryxell, Eric Myra Flash Center – University of Chicago o Milad Fatenejad, Don Lamb, Carlo Grazianni Los Alamos National Laboratory o Chris Fryer, John Wohlbier

The CRASH problem has inspired this collaboration When output from H2D at 1.1 ns is used as the initial conditions for CRASH, the primary shock is not planar, but shows a large protruding feature at the center of the tube Wall shock appears similar to that seen in experiments

We are comparing several HEDP codes Codes currently in the test suite o CRASH (University of Michigan) o FLASH (University of Chicago) o RAGE, CASSIO (LANL) o HYDRA (LLNL) Our goal is to understand differences between results of the CRASH experiment and simulations This will be accomplished by comparing the codes on a wide range of problems, from simple tests to full HEDP experiments

The codes in the test suite cover a range of numerical algorithms and physics models Grid o CRASH – Eulerian AMR, block structured o FLASH – Eulerian AMR, block structured o RAGE/CASSIO – Eulerian AMR, cell-by-cell refinement o HYDRA – ALE (Arbitrary Lagrangian-Eulerian) Hydrodynamics o CRASH – Second-order Godunov, dimensionally unsplit o FLASH – Piecewise-Parabolic Method, Strang splitting o RAGE/CASSIO – Second-order Godunov o HYDRA – Lagrangian with remap

Treatment of material interfaces differs significantly between the codes CRASH o Level set method – no mixed cells FLASH o Separate advection equation for each species o Interface steepener - consistent mass advection algorithm o Opacities in mixed cells weighted by number density o Common T i in each cell used to compute other quantities RAGE/CASSIO o Interface preserver or volume of fluid o Opacities in mixed cells weighted by number density o EOS in mixed cells assume temperature and pressure equilibration HYDRA o No mixed cells in Lagrangian mode

Both radiative diffusion and transport are represented in the test suite Radiative Transfer o CRASH / FLASH / RAGE  Multigroup flux-limited diffusion  Emission term treated explicitly (implicitly in CRASH)  Equations for electron energy and each radiation group advanced separately  CRASH includes frequency advection  RAGE uses implicit gray calculation for radiation/plasma energy exchange o CASSIO  Implicit Monte Carlo o HYDRA  Multigroup flux-limited diffusion  Emission term treated implicitly  Equations for electron energy and each radiation group advanced simultaneously  Implicit Monte Carlo (not yet exercised for this study)

A variety of three-temperature methods and drive sources are included Three-temperature approach o CRASH / FLASH / RAGE / CASSIO  Compression/shock heating divided among ions, electron, and radiation in proportion to pressure ratios  FLASH has option to solve separate electron entropy equation to apply shock heating only to ions o HYDRA  Only ions are shock heated by adding an artificial viscous pressure to the ion pressure Drive source o CRASH – Laser drive from Hyades, X-ray drive, laser package o FLASH – X-ray drive, laser package under development o RAGE – X-ray drive, laser package under development o CASSIO – Mono-energetic photons o HYDRA – Single-beam laser

First code comparison attempt was the “1d shifted problem” One-dimensional version of the CRASH problem shifted into a frame of reference in which the Be disk is stationary

The first attempt showed significant differences in shock structure between RAGE and FLASH

Results on 1D shifted problem have led us to consider a suite of simpler tests Temperature relaxation tests Diffusion tests o Conduction o Radiative diffusion Hydrodynamic tests These tests are still in progress – some tests have been completed with only a subset of the code suite, while others have not yet been attempted with any of the codes

Temperature relaxation tests Initial conditions o Infinite Medium – no spatial gradients o Ion, electron, and radiation temperatures initialized to different values o Fully ionized helium plasma with density gm/cm 3 o Gamma-law EOS Individual tests o Ion/Electron equilibration o Ion/Electron equilibration + radiation  Constant opacity  Electron-temperature-dependent opacity  Energy-group-dependent opacity 4 groups or 8 groups Constant (but different) opacity in each group

CRASH, FLASH and RAGE give identical results for the simplest relaxation problems Ion-electron equilibration Ion-electron-radiation equilibration

RAGE and FLASH show differences in multigroup tests 8 energy groups – constant but different opacity in each group Significant differences in energy density in each group Smaller differences in temperatures Differences not yet understood Comparison with future CRASH results may help track down differences

Diffusion tests 1) Electron conduction 2) Electron conduction + ion/electron equilibration 3) Gray radiation diffusion 4) Electron conduction + ion/electron equilibration + gray radiation diffusion 5) Electron conduction + ion/electron equilibration + multigroup radiation diffusion 6) Tests run with and without flux limiters

Electron conduction test led to discovery of bug in FLASH Initial temperature profile Before bug fix in FLASHAfter bug fix in FLASH t = 1.5 ns

Codes agree on diffusion tests 2) and 3) Conduction + ion/electron couplingGray radiation diffusion All three codes give identical results t = 1.5 ns t = 2.e-5 ns

Codes still agree with “full physics” Gray diffusion, emission/absorption, electron conduction, electron/ion coupling t = 0.2 ns

Hydrodynamics tests – not yet completed Hydrodynamics (shifted 1d simulations) o Hydro + ion/electron equilibration o Hydro + electron conduction o Hydro + radiation diffusion + electron conduction

We have learned a great deal from these simple test problems As a result of these tests we were able to o Understand some of the differences in the codes more clearly o Find bugs in codes o Improve the physics models within the codes o Test physics that is difficult to verify using analytic solutions o Understand time step size requirements for each type of physics

Xe opacity comparisons Data plotted for a single matter temperature and density relevant to the CRASH experiment Relevant photon energies are those below ~300 eV. T = 50 eV, r=0.011 gm/cm 3

Magnified view of relevant region T = 50 eV, r=0.011 gm/cm 3

Shock morphology is sensitive to Xe opacity Simulations used SESAME gray opacities Xe opacities multiplied by constant scale factor of 1, 10, and 100 For future studies, different scale factors may be used for each energy group

More complex comparisons Two-dimensional shifted simulations with X-ray drive Two-dimensional simulations of full CRASH experiment with X-ray drive Two-dimensional simulations of full CRASH experiment with input from H2D with laser drive Two-dimensional simulations of full CRASH experiment with self-contained laser drive

Tuning CRASH with X-ray drive can eliminate axis feature These two simulations are identical except for the temperature of the X-ray drive

Initial untuned FLASH simulation with X-ray drive produces the anomalous axis feature Initiated with mono-energetic X-ray drive Time = 6 ns

Low grid resolution can produce misleading results CASSIO initiated with X-ray drive (mono-energetic photons) No protruding axis feature at low resolution CASSIO

High-resolution untuned CASSIO simulation with IMC transport produces axis feature Initiated with X-ray drive (mono-energetic photons) time = 15 ns High resolution – 1.5 micron Protruding feature on axis is present

Low resolution HYDRA simulation with laser drive produces a small axis feature 30 ns Higher resolution simulation is needed before definitive conclusion can be reached about the axis feature

CRASH hydrodynamic validation study Jacobs’ Richtmyer-Meshkov instability experiment o Instability generated by shock impulsively accelerating an interface between two materials o Sinusoidal perturbation of interface – amplitude grows in time o Performed in vertical shock tube o Materials used were air and SF 6 (density ratio ~ 1:5) o Shock Mach number = 1.21 o Shock reflects from end of tube and re-shocks the interface

Results at 6 ms (before re-shock) 128 grid points per wavelength 256 grid points per wavelength ExperimentExperiment shows more roll up than simulations

Growth rate agrees well with experiment Re-shock

Summary Detailed comparisons of five HEDP codes have begun Good agreement on many test problems Discrepancies still exist for some simple test problems Comparisons have already led to the discovery of a number of bugs and code improvements Non-planar primary shock has been seen in simulations of the CRASH experiment at high resolution using four of the codes in the test suite Validation simulations of Richtmyer-Meshkov instabilities produced good agreement with Jacobs’ experiments – especially before re-shock