Collaborative Comparison of High-Energy-Density

Physics CodesLA-UR-12-20929

Bruce FryxellCenter for Radiative Shock HydrodynamicsDept. of Atmospheric, Oceanic and Space

SciencesUniversity of Michigan

HEDLA 2012Florida State University

Tallahassee, FLMay 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 DEFC52-08NA28616.

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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

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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

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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 Te and Ti 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

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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

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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

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1d radiative shock problem – initial results

Shock structure initially differed significantlybetween FLASH and RAGE

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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

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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 0.0065 gm/cm3

– 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

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Single-group temperature equilibration tests

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Ion-electron equilibration Ion-electron-radiation equilibration

CRASH, FLASH and RAGE give identical results for the simplest relaxation problems

8 Groups constant opacity

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Same opacity used for each group

CRASH, FLASH, and RAGE all agree extremely well

4-group temperature equilibration

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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

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Electron conduction test

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Initial temperature

profile

Before bug fix in FLASH

After bug fix in FLASH

More diffusion tests

Conduction + ion/electron coupling Gray radiation diffusion

All three codes give identical results

Diffusion tests

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Gray radiation diffusion, electron conduction, emission/absorption, electron-

ion equilibration

Tests with hydrodynamics

• Shafranov problem – Steady shock in a two-temperature plasma with Te ≠ Ti

– Includes electron thermal conduction and ion–electron equilibration

– Analytic solution exists– Upstream conditions:

» ρ = 0.0018 g/cc

» Te = 40 eV

» Ti = 40 eV

» Vx = 0 cm/s

– Downstream conditions» ρ = 0.004466 g/cc

» Te = 102.4393 eV

» Ti = 102.4393 eV

» Vx = 9.9635 x 106 cm/s

– Fully ionized helium (ϒ = 5/3 gas)– Shock speed = 1.6234 x 107 cm/s

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Shafranov problem - results

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Peak ion temperatureAnalytic – 124.2

evFLASH – 122.8

evCRASH – 122.5

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

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