Collaborative Comparison of High-Energy-Density Physics Codes LA-UR Bruce Fryxell Center for Radiative Shock Hydrodynamics Dept. of Atmospheric, Oceanic and Space Sciences University of Michigan HEDLA 2012 Florida State University Tallahassee, FL May 1, 2012

Code collaboration participants CRASH – University of Michigan –Bruce Fryxell, Eric Myra Flash Center – University of Chicago –Milad Fatenejad, Don Lamb, Carlo Grazianni Los Alamos National Laboratory –Chris Fryer, John Wohlbier This research was supported at the University of Michigan by the DOE NNSA under the Predictive Science Academic Alliance Program by grant number DEFC52-08NA

Goal of collaboration To compare several simulation codes containing the physics necessary to model high-energy-density physics experiments on a number of problems ranging from simple test problems to full experiments Codes currently in the test suite –CRASH (University of Michigan) –FLASH (University of Chicago) –RAGE (LANL) Initial simple test problems will compare temperature equilibration, diffusion, and hydrodynamics modules Future studies to compare additional physics modules of the codes (e.g. laser package, MHD, …) are being considered 3

Description of codes in the test suite Grid –CRASH – Eulerian AMR, block structured –FLASH – Eulerian AMR, block structured –RAGE – Eulerian AMR, cell-by-cell refinement Hydrodynamics –CRASH – Second-order Godunov –FLASH – Piecewise-Parabolic Method –RAGE – Second-order Godunov 4

Description of codes in the test suite Treatment of material interfaces –CRASH »Level set method – no mixed cells –FLASH »Separate advection equation for each species »Interface steepener - consistent mass advection algorithm »Opacities in mixed cells weighted by number density »Common T e and T i in each cell used to compute other quantities –RAGE »Interface preserver or volume of fluid »Opacities in mixed cells weighted by number density »EOS in mixed cells assume temperature and pressure equilibration 5

Description of codes in the test suite Radiative Transfer –CRASH / FLASH / RAGE »Flux-limited multigroup diffusion »Equations for electron energy and each radiation group advanced separately »CRASH includes Doppler shifting of frequencies »RAGE uses implicit gray calculation for radiation/plasma energy exchange Three temperature approach –CRASH / FLASH / RAGE »Separate equations for total energy, electron energy (electron pressure in CRASH), and radiation energy »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 6

Code-to-code comparisons – radiative shock First attempt was to compare codes on a simple one-dimensional reverse radiative shock problem generated by supersonic flow into a wall 7

1d radiative shock problem – initial results Shock structure initially differed significantly between FLASH and RAGE 8

Simple code-to-code comparison tests Because of these discrepancies, we decided to run even simpler test problems to attempt to understand the differences between the codes As a result of these tests we were able to –Understand some of the differences in the codes more clearly –Find bugs in codes –Improve the physics models within the codes –Test physics that is difficult to verify using analytic solutions 9

Temperature relaxation tests Initial conditions –Infinite medium – no spatial gradients –Ion, electron, and radiation temperatures initialized to different values –Fully ionized helium plasma with density gm/cm 3 –Gamma-law EOS Individual tests –Ion–electron equilibration –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 10

Single-group temperature equilibration tests 11 Ion-electron equilibrationIon-electron-radiation equilibration CRASH, FLASH and RAGE give identical results for the simplest relaxation problems

8 Groups constant opacity 12 Same opacity used for each group CRASH, FLASH, and RAGE all agree extremely well

4-group temperature equilibration 13 Constant, but different opacity in each group Initially, RAGE results differed from CRASH and FLASH results. RAGE has since been corrected and now agrees with the other two codes. Energy in each group vs. time Initial difference in RAGE results

Diffusion tests Electron conduction Electron conduction + ion/electron equilibration Gray radiation diffusion Electron conduction + ion/electron equilibration + gray radiation diffusion Electron conduction + ion/electron equilibration + multigroup radiation diffusion 14

Electron conduction test 15 Initial temperature profile Before bug fix in FLASHAfter bug fix in FLASH

More diffusion tests Conduction + ion/electron coupling Gray radiation diffusion All three codes give identical results

Diffusion tests 17 Gray radiation diffusion, electron conduction, emission/absorption, electron-ion equilibration

Tests with hydrodynamics Shafranov problem –Steady shock in a two-temperature plasma with T e ≠ T i –Includes electron thermal conduction and ion–electron equilibration –Analytic solution exists –Upstream conditions: »ρ = g/cc »T e = 40 eV »T i = 40 eV »V x = 0 cm/s –Downstream conditions »ρ = g/cc »T e = eV »T i = eV »V x = x 10 6 cm/s –Fully ionized helium ( ϒ = 5/3 gas) – Shock speed = x 10 7 cm/s 18

Shafranov problem - results 19 Peak ion temperature Analytic – ev FLASH – ev CRASH – ev

Conclusions Detailed comparisons of HEDP codes have begun Good agreement on many test problems Minor discrepancies still exist for some simple test problems Comparisons have already led to the discovery of a number of bugs and code improvements More complex tests remain to be completed 20