## Implicit Monte Carlo with a linear discontinuous finite element material solution and piecewise non-constant opacity

## Abstract

Here, the non-linear thermal radiative-transfer equations can be solved in various ways. One popular way is the Fleck and Cummings Implicit Monte Carlo (IMC) method. The IMC method was originally formulated with piecewise-constant material properties. For domains with a coarse spatial grid and large temperature gradients, an error known as numerical teleportation may cause artificially non-causal energy propagation and consequently an inaccurate material temperature. Source tilting is a technique to reduce teleportation error by constructing sub-spatial-cell (or sub-cell) emission profiles from which IMC particles are sampled. Several source tilting schemes exist, but some allow teleportation error to persist. We examine the effect of source tilting in problems with a temperature-dependent opacity. Within each cell, the opacity is evaluated continuously from a temperature profile implied by the source tilt. For IMC, this is a new approach to modeling the opacity. We find that applying both source tilting along with a source tilt-dependent opacity can introduce another dominant error that overly inhibits thermal wavefronts. We show that we can mitigate both teleportation and under-propagation errors if we discretize the temperature equation with a linear discontinuous (LD) trial space. Our method is for opacities ~ 1/T ^{3}, but we formulate and test amore »

- Authors:

- Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
- Bettis Atomic Power Lab., West Mifflin, PA (United States)

- Publication Date:

- Research Org.:
- Los Alamos National Lab. (LANL), Los Alamos, NM (United States)

- Sponsoring Org.:
- USDOE

- OSTI Identifier:
- 1255243

- Report Number(s):
- LA-UR-15-24303

Journal ID: ISSN 2332-4309

- Grant/Contract Number:
- AC52-06NA25396

- Resource Type:
- Accepted Manuscript

- Journal Name:
- Journal of Computational and Theoretical Transport

- Additional Journal Information:
- Journal Volume: 141; Journal Issue: C; Journal ID: ISSN 2332-4309

- Publisher:
- Taylor and Francis

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 97 MATHEMATICS AND COMPUTING; 73 NUCLEAR PHYSICS AND RADIATION PHYSICS; radiation, transport, methods

### Citation Formats

```
Wollaeger, Ryan T., Wollaber, Allan B., Urbatsch, Todd J., and Densmore, Jeffery D. Implicit Monte Carlo with a linear discontinuous finite element material solution and piecewise non-constant opacity. United States: N. p., 2016.
Web. doi:10.1080/23324309.2016.1157491.
```

```
Wollaeger, Ryan T., Wollaber, Allan B., Urbatsch, Todd J., & Densmore, Jeffery D. Implicit Monte Carlo with a linear discontinuous finite element material solution and piecewise non-constant opacity. United States. doi:10.1080/23324309.2016.1157491.
```

```
Wollaeger, Ryan T., Wollaber, Allan B., Urbatsch, Todd J., and Densmore, Jeffery D. Tue .
"Implicit Monte Carlo with a linear discontinuous finite element material solution and piecewise non-constant opacity". United States. doi:10.1080/23324309.2016.1157491. https://www.osti.gov/servlets/purl/1255243.
```

```
@article{osti_1255243,
```

title = {Implicit Monte Carlo with a linear discontinuous finite element material solution and piecewise non-constant opacity},

author = {Wollaeger, Ryan T. and Wollaber, Allan B. and Urbatsch, Todd J. and Densmore, Jeffery D.},

abstractNote = {Here, the non-linear thermal radiative-transfer equations can be solved in various ways. One popular way is the Fleck and Cummings Implicit Monte Carlo (IMC) method. The IMC method was originally formulated with piecewise-constant material properties. For domains with a coarse spatial grid and large temperature gradients, an error known as numerical teleportation may cause artificially non-causal energy propagation and consequently an inaccurate material temperature. Source tilting is a technique to reduce teleportation error by constructing sub-spatial-cell (or sub-cell) emission profiles from which IMC particles are sampled. Several source tilting schemes exist, but some allow teleportation error to persist. We examine the effect of source tilting in problems with a temperature-dependent opacity. Within each cell, the opacity is evaluated continuously from a temperature profile implied by the source tilt. For IMC, this is a new approach to modeling the opacity. We find that applying both source tilting along with a source tilt-dependent opacity can introduce another dominant error that overly inhibits thermal wavefronts. We show that we can mitigate both teleportation and under-propagation errors if we discretize the temperature equation with a linear discontinuous (LD) trial space. Our method is for opacities ~ 1/T3, but we formulate and test a slight extension for opacities ~ 1/T3.5, where T is temperature. We find our method avoids errors that can be incurred by IMC with continuous source tilt constructions and piecewise-constant material temperature updates.},

doi = {10.1080/23324309.2016.1157491},

journal = {Journal of Computational and Theoretical Transport},

number = C,

volume = 141,

place = {United States},

year = {2016},

month = {2}

}

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