# Piecewise linear discretization of Symbolic Implicit Monte Carlo radiation transport in the difference formulation

## Abstract

We describe a Monte Carlo solution for time dependent photon transport, in the difference formulation with the material in local thermodynamic equilibrium, that is piecewise linear in its treatment of the material state variable. Our method employs a Galerkin solution for the material energy equation while using Symbolic Implicit Monte Carlo to solve the transport equation. In constructing the scheme, one has the freedom to choose between expanding the material temperature, or the equivalent black body radiation energy density at the material temperature, in terms of finite element basis functions. The former provides a linear treatment of the material energy while the latter provides a linear treatment of the radiative coupling between zones. Subject to the conditional use of a lumped material energy in the vicinity of strong gradients, possible with a linear treatment of the material energy, our approach provides a robust solution for time dependent transport of thermally emitted radiation that can address a wide range of problems. It produces accurate results in thick media.

- Authors:

- University of California, Lawrence Livermore National Laboratory, P.O. Box 808, Livermore, CA 94550 (United States). E-mail: brooks3@llnl.gov
- University of California, Lawrence Livermore National Laboratory, P.O. Box 808, Livermore, CA 94550 (United States)

- Publication Date:

- OSTI Identifier:
- 20840372

- Resource Type:
- Journal Article

- Resource Relation:
- Journal Name: Journal of Computational Physics; Journal Volume: 220; Journal Issue: 1; Other Information: DOI: 10.1016/j.jcp.2006.07.014; PII: S0021-9991(06)00343-3; Copyright (c) 2006 Elsevier Science B.V., Amsterdam, The Netherlands, All rights reserved; Country of input: International Atomic Energy Agency (IAEA)

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; BLACKBODY RADIATION; ENERGY DENSITY; EQUATIONS; FINITE ELEMENT METHOD; LTE; MONTE CARLO METHOD; PHOTON TRANSPORT; TIME DEPENDENCE; TRANSPORT THEORY

### Citation Formats

```
Brooks, Eugene D., Szoke, Abraham, and Peterson, Jayson D.L..
```*Piecewise linear discretization of Symbolic Implicit Monte Carlo radiation transport in the difference formulation*. United States: N. p., 2006.
Web. doi:10.1016/j.jcp.2006.07.014.

```
Brooks, Eugene D., Szoke, Abraham, & Peterson, Jayson D.L..
```*Piecewise linear discretization of Symbolic Implicit Monte Carlo radiation transport in the difference formulation*. United States. doi:10.1016/j.jcp.2006.07.014.

```
Brooks, Eugene D., Szoke, Abraham, and Peterson, Jayson D.L.. Wed .
"Piecewise linear discretization of Symbolic Implicit Monte Carlo radiation transport in the difference formulation". United States.
doi:10.1016/j.jcp.2006.07.014.
```

```
@article{osti_20840372,
```

title = {Piecewise linear discretization of Symbolic Implicit Monte Carlo radiation transport in the difference formulation},

author = {Brooks, Eugene D. and Szoke, Abraham and Peterson, Jayson D.L.},

abstractNote = {We describe a Monte Carlo solution for time dependent photon transport, in the difference formulation with the material in local thermodynamic equilibrium, that is piecewise linear in its treatment of the material state variable. Our method employs a Galerkin solution for the material energy equation while using Symbolic Implicit Monte Carlo to solve the transport equation. In constructing the scheme, one has the freedom to choose between expanding the material temperature, or the equivalent black body radiation energy density at the material temperature, in terms of finite element basis functions. The former provides a linear treatment of the material energy while the latter provides a linear treatment of the radiative coupling between zones. Subject to the conditional use of a lumped material energy in the vicinity of strong gradients, possible with a linear treatment of the material energy, our approach provides a robust solution for time dependent transport of thermally emitted radiation that can address a wide range of problems. It produces accurate results in thick media.},

doi = {10.1016/j.jcp.2006.07.014},

journal = {Journal of Computational Physics},

number = 1,

volume = 220,

place = {United States},

year = {Wed Dec 20 00:00:00 EST 2006},

month = {Wed Dec 20 00:00:00 EST 2006}

}