# The Transport Equation in Optically Thick Media: Discussion of IMC and its Diffusion Limit

## Abstract

We discuss the limits of validity of the Implicit Monte Carlo (IMC) method for the transport of thermally emitted radiation. The weakened coupling between the radiation and material energy of the IMC method causes defects in handling problems with strong transients. We introduce an approach to asymptotic analysis for the transport equation that emphasizes the fact that the radiation and material temperatures are always different in time-dependent problems, and we use it to show that IMC does not produce the correct diffusion limit. As this is a defect of IMC in the continuous equations, no improvement to its discretization can remedy it.

- Authors:

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

- Publication Date:

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

- Sponsoring Org.:
- USDOE

- OSTI Identifier:
- 1289358

- Report Number(s):
- LLNL-TR-697860

- DOE Contract Number:
- AC52-07NA27344

- Resource Type:
- Technical Report

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; Implicit Monte Carlo; Radiation transport; Diffusion limit

### Citation Formats

```
Szoke, A., and Brooks, E. D..
```*The Transport Equation in Optically Thick Media: Discussion of IMC and its Diffusion Limit*. United States: N. p., 2016.
Web. doi:10.2172/1289358.

```
Szoke, A., & Brooks, E. D..
```*The Transport Equation in Optically Thick Media: Discussion of IMC and its Diffusion Limit*. United States. doi:10.2172/1289358.

```
Szoke, A., and Brooks, E. D.. Tue .
"The Transport Equation in Optically Thick Media: Discussion of IMC and its Diffusion Limit". United States. doi:10.2172/1289358. https://www.osti.gov/servlets/purl/1289358.
```

```
@article{osti_1289358,
```

title = {The Transport Equation in Optically Thick Media: Discussion of IMC and its Diffusion Limit},

author = {Szoke, A. and Brooks, E. D.},

abstractNote = {We discuss the limits of validity of the Implicit Monte Carlo (IMC) method for the transport of thermally emitted radiation. The weakened coupling between the radiation and material energy of the IMC method causes defects in handling problems with strong transients. We introduce an approach to asymptotic analysis for the transport equation that emphasizes the fact that the radiation and material temperatures are always different in time-dependent problems, and we use it to show that IMC does not produce the correct diffusion limit. As this is a defect of IMC in the continuous equations, no improvement to its discretization can remedy it.},

doi = {10.2172/1289358},

journal = {},

number = ,

volume = ,

place = {United States},

year = {2016},

month = {7}

}

Save to My Library

You must Sign In or Create an Account in order to save documents to your library.