# Corrected Implicit Monte Carlo

## Abstract

Here in this work we develop a set of nonlinear correction equations to enforce a consistent time-implicit emission temperature for the original semi-implicit IMC equations. We present two possible forms of correction equations: one results in a set of non-linear, zero-dimensional, non-negative, explicit correction equations, and the other results in a non-linear, non-negative, Boltzman transport correction equation. The zero-dimensional correction equations adheres to the maximum principle for the material temperature, regardless of frequency-dependence, but does not prevent maximum principle violation in the photon intensity, eventually leading to material overheating. The Boltzman transport correction guarantees adherence to the maximum principle for frequency-independent simulations, at the cost of evaluating a reduced source non-linear Boltzman equation. Finally, we present numerical evidence suggesting that the Boltzman transport correction, in its current form, significantly improves time step limitations but does not guarantee adherence to the maximum principle for frequency-dependent simulations.

- Authors:

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

- Publication Date:

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

- Sponsoring Org.:
- USDOE National Nuclear Security Administration (NNSA)

- OSTI Identifier:
- 1416278

- Report Number(s):
- LA-UR-17-22796

Journal ID: ISSN 0021-9991; TRN: US1800892

- Grant/Contract Number:
- AC52-06NA25396

- Resource Type:
- Journal Article: Accepted Manuscript

- Journal Name:
- Journal of Computational Physics

- Additional Journal Information:
- Journal Volume: 359; Journal ID: ISSN 0021-9991

- Publisher:
- Elsevier

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 97 MATHEMATICS AND COMPUTING; Thermal radiative transfer; Implicit Monte Carlo; HOLO

### Citation Formats

```
Cleveland, Mathew Allen, and Wollaber, Allan Benton.
```*Corrected Implicit Monte Carlo*. United States: N. p., 2018.
Web. doi:10.1016/j.jcp.2017.12.038.

```
Cleveland, Mathew Allen, & Wollaber, Allan Benton.
```*Corrected Implicit Monte Carlo*. United States. doi:10.1016/j.jcp.2017.12.038.

```
Cleveland, Mathew Allen, and Wollaber, Allan Benton. Tue .
"Corrected Implicit Monte Carlo". United States.
doi:10.1016/j.jcp.2017.12.038.
```

```
@article{osti_1416278,
```

title = {Corrected Implicit Monte Carlo},

author = {Cleveland, Mathew Allen and Wollaber, Allan Benton},

abstractNote = {Here in this work we develop a set of nonlinear correction equations to enforce a consistent time-implicit emission temperature for the original semi-implicit IMC equations. We present two possible forms of correction equations: one results in a set of non-linear, zero-dimensional, non-negative, explicit correction equations, and the other results in a non-linear, non-negative, Boltzman transport correction equation. The zero-dimensional correction equations adheres to the maximum principle for the material temperature, regardless of frequency-dependence, but does not prevent maximum principle violation in the photon intensity, eventually leading to material overheating. The Boltzman transport correction guarantees adherence to the maximum principle for frequency-independent simulations, at the cost of evaluating a reduced source non-linear Boltzman equation. Finally, we present numerical evidence suggesting that the Boltzman transport correction, in its current form, significantly improves time step limitations but does not guarantee adherence to the maximum principle for frequency-dependent simulations.},

doi = {10.1016/j.jcp.2017.12.038},

journal = {Journal of Computational Physics},

number = ,

volume = 359,

place = {United States},

year = {Tue Jan 02 00:00:00 EST 2018},

month = {Tue Jan 02 00:00:00 EST 2018}

}