A comparison of radiation transport and diffusionusing PDT and the CRASH code

Fall 2011 Review

Eric S. MyraWm. Daryl Hawkins

Our goal is to quantify error associated with using flux-limited diffusion in CRASH

Key goals:

• Using PDT and CRASH, perform “method verification,” with the aim of improving the implementation of radiation diffusion and better understanding its shortcomings

• As necessary, perform code-to-code comparison and verification in the diffusion regime

• To the extent possible, set up the full CRASH problem in both codes and quantify the uncertainty of using diffusion vs. full transport

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• This study was recommended by the 2010 Review Committee

• PDT/CRASH coupling not presently an option

An objective comparison oftransport and diffusion is challenging

• Differences in

— discretization and solution methods

— phase space coverage (full vs. a subset)

— treatment of multiphysics coupling (e.g., matter-radiation energy exchange)

• Characterizing the effects of ad hoc features of a model

— flux limiters in diffusion

— use of microphysics (e.g., opacities)

• Procedural differences

— e.g., the code may be used for a test problem in a different mode than for “real” problems (timestep selection, use of converged temperatures, etc.)

• A problem that’s easy for one code can be difficult for the other

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Flux-limited diffusion approximates transport

The full transport equation (used by PDT).

The radiation energy equation (used by CRASH) is the zeroth angular moment of the transport equation with diffusive closure attained by Fick’s law.

with and

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Flux-limited diffusion approximates transport

The full transport equation (used by PDT).

The radiation energy equation (used by CRASH) is the zeroth angular moment of the transport equation with diffusive closure attained by Fick’s law.

with and

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Target problems determine how we use each code

PDT: a deterministic radiation transport code• Rad energy: gray and multigroup (both used)

• Rad angle: discrete ordinates (256 angles used)

• Spatial: discontinuous finite element method

• Time: fully implicit

CRASH: an Eulerian rad-hydro, flux-limited-diffusion code• Rad energy: gray and multigroup (both used)

• Rad angle: angle-averaged—0th angular moment equation, with 1st angular moment equation replaced by flux-limited diffusion

• Spatial: finite volume method

• Time: fully implicit

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The starting point for comparison isdiffusion-limit test problems

• Gray transport

• Simple opacities, but which may vary sharply across an interface

• Examples:

— Infinite medium problems to test rates

— Front problems to test wave propagation

— Marshak waves to test propagation and rates

— Added heat sources as a proxy for shock heating

• Concerns:

— Choosing physically relevant timescales

— Computationally tractable in a reasonable time by both codes

— Defining “diffusive” for purposes of code comparison

If done with care, the codes should agree closely

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Both codes advance a diffusive front similarly

• Gray transport

• Uniform density of 1 g cm-3

• Opacity = 105 cm2 g-1 in strip

• Opacity = 104 cm2 g-1 outside, but no emission-absorption

Te

Trad = 1 eV

Initial conditions

Results for radiationAt t = 3.0 ps…

• Results for each code are virtually identical for Trad

(PDT in maroon; CRASH in blue dashes)

• Te unchanged for both

• tdiff ~ 10 ns, tfs ~ 3.0 ps,

therefore diffusive8

A Marshak wave with a heat source also agrees well

• Gray transport

• Uniform density of 1 g cm-3

• Opacity = 105 cm2 g-1 in strip

• Opacity = 103 cm2 g-1 outside

• Emission-absorption active everywhere

• dQ/dt = 4.25 x 1033 eV cm-3 s-1 in central strip

Te

Trad = 1 eV

Initial conditions

At t = 100 ps, agreement is good

Material energy transport matches

Volume vs. surface effect?

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PDTCRASH

Q added

A more realistic test problem has been formulated

0.10 cm 0.08 cm 0.20 cm

0.02 cm0.05 cm

Plastic

Plastic

Au

Au

Be:higher opacity

Post-shock

Xe

Pre-shockXe:

lower opacity

Sh

oc

ke

d X

e

0.0025 cm

0.0025 cm

0.0575 cm

• Hydrostatic

• 2D Cartesian

• No heat conduction

• Realistic opacities, using the CRASH tables

• A heat source acts as a proxy for shock heating

• Te = Trad = 1.0 eV, initially

• Cv (Xe, Au) = 9.9 x 1017 eV g-1 K-1

• Cv (Be, Pl) = 1.1 x 1019 eV g-1 K-1

• dQ/dt = 4.25 x 1033 eV cm-3 s-1

opacitycliff

The heat source is active within this region

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A 1D gray version of the problem provides a first look

t = 2.0 ps t = 5.0 ps

t = 20.0 ps t = 50.0 ps

____ CRASH FLD on

_ _ _ CRASH FLD off

____ PDT Transport

Trad shows only qualitative agreement on this problem

t = 50.0 ps

Material energy transport differs

significantly

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Agreement starts to improve in1D multigroup comparisons

____ CRASH FLD on

____ PDT Transport

Trad shows good agreement at early

times, then starts to diverge

• Material energy transport still

differs significantly.• However, in multigroup, PDT now

moves more energy, esp. upstream

“Upstream” radiative pre-

heating

t = 2.0 ps t = 5.0 ps

t = 20.0 ps t = 50.0 ps

t = 50.0 ps

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10 groups, geometrically spaced, 1.0 eV–20 keV

These results suggest some next steps

• 1D Xe-on-polyimide problem—relevant to wall ablation

• Complete the suite of runs using the 2D version of the CRASH setup

• Implement a second problem using snapshots from full-system CRASH rad-hydro runs as initial conditions.

— Provides more realistic initial conditions (e.g., temperatures)

— Mitigates initial transients and uncertainties in the appropriate timescale over which to make comparisons

— Allows direct comparison between successive rad-hydro CRASH timesteps and PDT

A preliminary 2D result using CRASH showing Trad

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Conclusions

• We have constructed a test environment that allows comparison of radiation transport and diffusion for problems relative to the CRASH.

• PDT and CRASH show good agreement on a set of problems where they should agree.

• PDT and CRASH show a mixture of agreement and discrepancy for more realistic CRASH-relevant problems.

• Further study is warranted to determine if these discrepancies are significant for predictive simulations of the CRASH experiment.

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