Code Comparison and ValidationLA-UR 11-04905

Bruce Fryxell

Center for Radiative Shock Hydrodynamics

Fall 2011 Review

Code comparison collaboration includes researchers from three institutions

CRASH – University of Michigano Bruce Fryxell, Eric Myra

Flash Center – University of Chicagoo Milad Fatenejad, Don Lamb, Carlo Grazianni

Los Alamos National Laboratoryo 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 suiteo 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

Grido 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)

Hydrodynamicso 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 Ti 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

HYDRAo 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 approacho 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 sourceo 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 testso 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 conditionso Infinite Medium – no spatial gradients

o Ion, electron, and radiation temperatures initialized to different values

o Fully ionized helium plasma with density 0.0065 gm/cm3

o Gamma-law EOS

Individual testso 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

temperaturesDifferences not yet understood

Comparison with future CRASH results may help track down differences

Diffusion tests1) 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 FLASH After bug fix in FLASH

t = 1.5 nst = 1.5 ns

Codes agree on diffusion tests 2) and 3)

Conduction + ion/electron coupling Gray 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 equilibrationo Hydro + electron conductiono 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 too 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/cm3

Magnified view of relevant region

T = 50 eV, r=0.011 gm/cm3

Shock morphology is sensitive to Xe opacity

Simulations used SESAME gray opacitiesXe 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 caneliminate 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 driveTime = 6 ns

Low grid resolution can producemisleading results

CASSIO initiated with X-ray drive (mono-energetic photons)No protruding axis feature at low resolution

CASSIO

High-resolution untuned CASSIO simulationwith IMC transport produces axis feature

Initiated with X-ray drive (mono-energetic photons)time = 15 ns

High resolution – 1.5 micronProtruding 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 experimento 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 SF6

(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

Experiment Experiment 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