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Title: A deterministic photon free method to solve radiation transfer equations

Abstract

A new method to solve radiation transfer equations is presented. In the absence of scattering, material motion, and heat conduction, the photon variables can be eliminated from the fully implicit, multi-group, discrete-ordinate, finite difference (finite element) equations of continuum radiation transfer to yield a smaller set of equations which depends only on temperature. The solution to this smaller set of equations is used to generate the solution to the original set of equations from which the reduced set is derived. The reduced system simplifies to a nonlinear heat equation in the regime of strong absorption and strong emission. We solve the reduced set of equations by the Newton-GMRES method in which the Jacobian update is preconditioned by a linearization of this nonlinear heat equation. The performances of this new method and of the semi-implicit linear method, which is preconditioned by grey transport acceleration combined with diffusion synthetic acceleration, are compared on two test problems. The test results indicate that the new method can take larger time steps, requires less memory, is more accurate, and is competitive in speed with the semi-implicit linear method.

Authors:
 [1]
  1. Center for Applied Scientific Computing, Lawrence Livermore National Laboratory, P.O. Box 808, L-561, Livermore, CA 94551 (United States)
Publication Date:
OSTI Identifier:
20991559
Resource Type:
Journal Article
Journal Name:
Journal of Computational Physics
Additional Journal Information:
Journal Volume: 222; Journal Issue: 1; Other Information: DOI: 10.1016/j.jcp.2006.06.048; PII: S0021-9991(06)00307-X; Copyright (c) 2006 Elsevier Science B.V., Amsterdam, The Netherlands, All rights reserved; Country of input: International Atomic Energy Agency (IAEA); Journal ID: ISSN 0021-9991
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; ABSORPTION; ACCELERATION; DETERMINISTIC ESTIMATION; DIFFUSION; DISCRETE ORDINATE METHOD; EMISSION; EQUATIONS; FINITE ELEMENT METHOD; NONLINEAR PROBLEMS; PHOTONS; RADIATION TRANSPORT; SCATTERING; THERMAL CONDUCTION; TRANSPORT THEORY

Citation Formats

Chang, Britton. A deterministic photon free method to solve radiation transfer equations. United States: N. p., 2007. Web. doi:10.1016/j.jcp.2006.06.048.
Chang, Britton. A deterministic photon free method to solve radiation transfer equations. United States. https://doi.org/10.1016/j.jcp.2006.06.048
Chang, Britton. 2007. "A deterministic photon free method to solve radiation transfer equations". United States. https://doi.org/10.1016/j.jcp.2006.06.048.
@article{osti_20991559,
title = {A deterministic photon free method to solve radiation transfer equations},
author = {Chang, Britton},
abstractNote = {A new method to solve radiation transfer equations is presented. In the absence of scattering, material motion, and heat conduction, the photon variables can be eliminated from the fully implicit, multi-group, discrete-ordinate, finite difference (finite element) equations of continuum radiation transfer to yield a smaller set of equations which depends only on temperature. The solution to this smaller set of equations is used to generate the solution to the original set of equations from which the reduced set is derived. The reduced system simplifies to a nonlinear heat equation in the regime of strong absorption and strong emission. We solve the reduced set of equations by the Newton-GMRES method in which the Jacobian update is preconditioned by a linearization of this nonlinear heat equation. The performances of this new method and of the semi-implicit linear method, which is preconditioned by grey transport acceleration combined with diffusion synthetic acceleration, are compared on two test problems. The test results indicate that the new method can take larger time steps, requires less memory, is more accurate, and is competitive in speed with the semi-implicit linear method.},
doi = {10.1016/j.jcp.2006.06.048},
url = {https://www.osti.gov/biblio/20991559}, journal = {Journal of Computational Physics},
issn = {0021-9991},
number = 1,
volume = 222,
place = {United States},
year = {Thu Mar 01 00:00:00 EST 2007},
month = {Thu Mar 01 00:00:00 EST 2007}
}