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}
}
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