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Title: An Evaluation of the Difference Formulation for Photon Transport in a Two Level System

Abstract

In this paper we extend the difference formulation for radiation transport to the case of a single atomic line. We examine the accuracy, performance and stability of the difference formulation within the framework of the Symbolic Implicit Monte Carlo method. The difference formulation, introduced for thermal radiation by some of the authors, has the unique property that the transport equation is written in terms that become small for thick systems. We find that the difference formulation has a significant advantage over the standard formulation for a thick system. The correct treatment of the line profile, however, requires that the difference formulation in the core of the line be mixed with the standard formulation in the wings and this may limit the advantage of the method. We bypass this problem by using the gray approximation. We develop three Monte Carlo solution methods based on different degrees of implicitness for the treatment of the source terms, and we find only conditional stability unless the source terms are treated fully implicitly.

Authors:
; ; ;
Publication Date:
Research Org.:
Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)
Sponsoring Org.:
US Department of Energy (US)
OSTI Identifier:
15015176
Report Number(s):
UCRL-JRNL-204366
Journal ID: ISSN 0021-9991; JCTPAH; TRN: US0501649
DOE Contract Number:  
W-7405-ENG-48
Resource Type:
Journal Article
Journal Name:
Journal of Computational Physics
Additional Journal Information:
Journal Volume: 204; Journal Issue: 1; Other Information: Journal publication date is March 20, 2005; PDF-FILE: 22 ; SIZE: 0.2 MBYTES; PBD: 20 May 2004; Journal ID: ISSN 0021-9991
Country of Publication:
United States
Language:
English
Subject:
73 NUCLEAR PHYSICS AND RADIATION PHYSICS; ACCURACY; EVALUATION; MONTE CARLO METHOD; PERFORMANCE; PHOTON TRANSPORT; RADIATION TRANSPORT; SOURCE TERMS; STABILITY; THERMAL RADIATION; TRANSPORT

Citation Formats

Daffin, F D, McKinley, M S, Brooks, E D, and Szoke, A. An Evaluation of the Difference Formulation for Photon Transport in a Two Level System. United States: N. p., 2004. Web. doi:10.1016/j.jcp.2004.09.014.
Daffin, F D, McKinley, M S, Brooks, E D, & Szoke, A. An Evaluation of the Difference Formulation for Photon Transport in a Two Level System. United States. https://doi.org/10.1016/j.jcp.2004.09.014
Daffin, F D, McKinley, M S, Brooks, E D, and Szoke, A. 2004. "An Evaluation of the Difference Formulation for Photon Transport in a Two Level System". United States. https://doi.org/10.1016/j.jcp.2004.09.014. https://www.osti.gov/servlets/purl/15015176.
@article{osti_15015176,
title = {An Evaluation of the Difference Formulation for Photon Transport in a Two Level System},
author = {Daffin, F D and McKinley, M S and Brooks, E D and Szoke, A},
abstractNote = {In this paper we extend the difference formulation for radiation transport to the case of a single atomic line. We examine the accuracy, performance and stability of the difference formulation within the framework of the Symbolic Implicit Monte Carlo method. The difference formulation, introduced for thermal radiation by some of the authors, has the unique property that the transport equation is written in terms that become small for thick systems. We find that the difference formulation has a significant advantage over the standard formulation for a thick system. The correct treatment of the line profile, however, requires that the difference formulation in the core of the line be mixed with the standard formulation in the wings and this may limit the advantage of the method. We bypass this problem by using the gray approximation. We develop three Monte Carlo solution methods based on different degrees of implicitness for the treatment of the source terms, and we find only conditional stability unless the source terms are treated fully implicitly.},
doi = {10.1016/j.jcp.2004.09.014},
url = {https://www.osti.gov/biblio/15015176}, journal = {Journal of Computational Physics},
issn = {0021-9991},
number = 1,
volume = 204,
place = {United States},
year = {Thu May 20 00:00:00 EDT 2004},
month = {Thu May 20 00:00:00 EDT 2004}
}

Works referenced in this record:

An implicit Monte Carlo scheme for calculating time and frequency dependent nonlinear radiation transport
journal, December 1971


An implicit Monte Carlo scheme for calculating time-dependent line transport
journal, November 1986


Asymptotic equilibrium diffusion analysis of time-dependent Monte Carlo methods for grey radiative transfer
journal, September 2004


Symbolic implicit Monte Carlo
journal, August 1989


The transport equation in optically thick media
journal, February 2005


Comparison of implicit and symbolic implicit Monte Carlo line transport with frequency weight vector extension
journal, July 2003