An evaluation of the difference formulation for photon transport in a two level system

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 f...

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Bibliographic Details
Published in:Journal of computational physics 2005-03, Vol.204 (1), p.27-45
Main Authors: Daffin, Frank, McKinley, Michael Scott, Brooks, Eugene D., Szöke, Abraham
Format: Article
Language:English
Subjects:
ACCURACY
CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS
Computational techniques
Difference formulation
EVALUATION
Exact sciences and technology
Implicit Monte Carlo
Line transport
Mathematical methods in physics
MATHEMATICAL SOLUTIONS
MONTE CARLO METHOD
PHOTON TRANSPORT
Physics
SOURCE TERMS
STABILITY
THERMAL RADIATION
TRANSPORT THEORY
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Summary: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.
ISSN:0021-9991
1090-2716
DOI:10.1016/j.jcp.2004.09.014