a comparison of radiation transport and diffusion using pdt and the crash code fall 2011 review
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A comparison of radiation transport and diffusion using PDT and the CRASH code Fall 2011 Review. Eric S. Myra Wm. Daryl Hawkins. Our goal is to quantify error associated with using flux-limited diffusion in CRASH. Key goals:

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a comparison of radiation transport and diffusion using pdt and the crash code fall 2011 review

A comparison of radiation transport and diffusionusing PDT and the CRASH codeFall 2011 Review

Eric S. Myra

Wm. Daryl Hawkins

our goal is to quantify error associated with using flux limited diffusion in crash
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
  • This study was recommended by the 2010 Review Committee
    • PDT/CRASH coupling not presently an option
an objective comparison of transport and diffusion is challenging
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

flux limited diffusion approximates transport
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

flux limited diffusion approximates transport1
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

5

target problems determine how we use each code
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

the starting point for comparison is diffusion limit test problems
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

both codes advance a diffusive front similarly
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 radiation

  • At 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 diffusive
a marshak wave with a heat source also agrees well
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-1outside

Emission-absorption active everywhere

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

Initial conditions

Te

Qadded

Trad = 1 eV

Volume vs. surface effect?

At t = 100 ps, agreement is good

PDT

CRASH

Material energy transport matches

a more realistic test problem has been formulated
A more realistic test problem has been formulated

Hydrostatic

2D Cartesian

No heat conduction

Realistic opacities, using the CRASH tables

A heat source acts as a proxy for shock heating

Plastic

0.0025 cm

Au

Post-

shock

Xe

Be:

higher opacity

Pre-shock

Xe:

lower opacity

0.0575 cm

Shocked Xe

The heat source is active within this region

Au

0.0025 cm

Plastic

0.20 cm

0.10 cm

0.08 cm

0.02 cm

0.05 cm

opacity

cliff

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

____CRASH FLD on

_ _ _CRASH FLD off

____PDT Transport

t = 2.0 ps

t = 5.0 ps

t = 50.0 ps

t = 20.0 ps

t = 50.0 ps

Material energy transport differs significantly

Trad shows only qualitative agreement on this problem

agreement starts to improve in 1d multigroup comparisons
Agreement starts to improve in1D multigroup comparisons

10 groups, geometrically spaced, 1.0 eV–20 keV

____CRASH FLD on

____PDT Transport

t = 5.0 ps

t = 2.0 ps

t = 50.0 ps

“Upstream” radiative pre-heating

t = 20.0 ps

t = 50.0 ps

  • Material energy transport still differs significantly.
  • However, in multigroup, PDT now moves more energy, esp. upstream

Trad shows good agreement at early times, then starts to diverge

these results suggest some next steps
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

conclusions
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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