# Benchmarks and models for 1-D radiation transport in stochastic participating media

## Abstract

Benchmark calculations for radiation transport coupled to a material temperature equation in a 1-D slab and 1-D spherical geometry binary random media are presented. The mixing statistics are taken to be homogeneous Markov statistics in the 1-D slab but only approximately Markov statistics in the 1-D sphere. The material chunk sizes are described by Poisson distribution functions. The material opacities are first taken to be constant and then allowed to vary as a strong function of material temperature. Benchmark values and variances for time evolution of the ensemble average of material temperature energy density and radiation transmission are computed via a Monte Carlo type method. These benchmarks are used as a basis for comparison with three other approximate methods of solution. One of these approximate methods is simple atomic mix. The second approximate model is an adaptation of what is commonly called the Levermore-Pomraning model and which is referred to here as the standard model. It is shown that recasting the temperature coupling as a type of effective scattering can be useful in formulating the third approximate model, an adaptation of a model due to Su and Pomraning which attempts to account for the effects of scattering in a stochasticmore »

- Authors:

- Univ. of California, Davis, CA (United States)

- Publication Date:

- Research Org.:
- Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)

- Sponsoring Org.:
- USDOE

- OSTI Identifier:
- 15013120

- Report Number(s):
- UCRL-LR-140199

TRN: US0600876

- DOE Contract Number:
- W-7405-ENG-48

- Resource Type:
- Thesis/Dissertation

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; 99 GENERAL AND MISCELLANEOUS//MATHEMATICS, COMPUTING, AND INFORMATION SCIENCE; BENCHMARKS; DISTRIBUTION FUNCTIONS; ENERGY DENSITY; GEOMETRY; HEATING; PERFORMANCE; RADIATION TRANSPORT; RADIATIONS; SCATTERING; STANDARD MODEL; STATISTICS

### Citation Formats

```
Miller, David Scott.
```*Benchmarks and models for 1-D radiation transport in stochastic participating media*. United States: N. p., 2000.
Web. doi:10.2172/15013120.

```
Miller, David Scott.
```*Benchmarks and models for 1-D radiation transport in stochastic participating media*. United States. doi:10.2172/15013120.

```
Miller, David Scott. Tue .
"Benchmarks and models for 1-D radiation transport in stochastic participating media". United States. doi:10.2172/15013120. https://www.osti.gov/servlets/purl/15013120.
```

```
@article{osti_15013120,
```

title = {Benchmarks and models for 1-D radiation transport in stochastic participating media},

author = {Miller, David Scott},

abstractNote = {Benchmark calculations for radiation transport coupled to a material temperature equation in a 1-D slab and 1-D spherical geometry binary random media are presented. The mixing statistics are taken to be homogeneous Markov statistics in the 1-D slab but only approximately Markov statistics in the 1-D sphere. The material chunk sizes are described by Poisson distribution functions. The material opacities are first taken to be constant and then allowed to vary as a strong function of material temperature. Benchmark values and variances for time evolution of the ensemble average of material temperature energy density and radiation transmission are computed via a Monte Carlo type method. These benchmarks are used as a basis for comparison with three other approximate methods of solution. One of these approximate methods is simple atomic mix. The second approximate model is an adaptation of what is commonly called the Levermore-Pomraning model and which is referred to here as the standard model. It is shown that recasting the temperature coupling as a type of effective scattering can be useful in formulating the third approximate model, an adaptation of a model due to Su and Pomraning which attempts to account for the effects of scattering in a stochastic context. This last adaptation shows consistent improvement over both the atomic mix and standard models when used in the 1-D slab geometry but shows limited improvement in the 1-D spherical geometry. Benchmark values are also computed for radiation transmission from the 1-D sphere without material heating present. This is to evaluate the performance of the standard model on this geometry--something which has never been done before. All of the various tests demonstrate the importance of stochastic structure on the solution. Also demonstrated are the range of usefulness and limitations of a simple atomic mix formulation.},

doi = {10.2172/15013120},

journal = {},

number = ,

volume = ,

place = {United States},

year = {2000},

month = {8}

}