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Title: 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:
 [1];  [2];  [2]
  1. University of California, Lawrence Livermore National Laboratory, P.O. Box 808, Livermore, CA 94550 (United States). E-mail: brooks3@llnl.gov
  2. 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}
}
  • We describe a Monte Carlo solution for time dependent photon transport, in the difference formulation with the material in local thermodynamic equilibrium (LTE), 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 (SIMC) 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 themore » 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 the diffusion limit.« less
  • The equations of radiation transport for thermal photons are notoriously difficult to solve in thick media without resorting to asymptotic approximations such as the diffusion limit. One source of this difficulty is that in thick, absorbing media, thermal emission and absorption are almost completely balanced. A new formulation for thermal radiation transport, called the difference formulation, was recently introduced in order to remove the stiff balance between emission and absorption. In the new formulation, thermal emission is replaced by derivative terms that become small in thick media. It was proposed that the difficulties of solving the transport equation in thickmore » media would be ameliorated by the difference formulation, while preserving full rigor and accuracy of the transport solution in the streaming limit. In this paper, the transport equation is solved by the symbolic implicit Monte Carlo method and comparisons are made between the standard formulation and the difference formulation. The method is easily adapted to the derivative source terms of the difference formulation, and a remarkable reduction in noise is obtained when the difference formulation is applied to problems involving thick media.« less
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