Accurate and efficient radiation transport in optically thick media -- by means of the Symbolic Implicit Monte Carlo method in the difference formulation

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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 is almost completely balanced by strong absorption. In a previous publication [SB03], the photon transport equation was written in terms of the deviation of the specific intensity from the local equilibrium field. We called the new form of the equations the difference formulation. The difference formulation is rigorously equivalent to the original transport equation. It is particularly advantageous in thick media, ... continued below

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Szoke, A; Brooks, E D; McKinley, M & Daffin, F March 30, 2005.

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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 is almost completely balanced by strong absorption. In a previous publication [SB03], the photon transport equation was written in terms of the deviation of the specific intensity from the local equilibrium field. We called the new form of the equations the difference formulation. The difference formulation is rigorously equivalent to the original transport equation. It is particularly advantageous in thick media, where the radiation field approaches local equilibrium and the deviations from the Planck distribution are small. The difference formulation for photon transport also clarifies the diffusion limit. In this paper, the transport equation is solved by the Symbolic Implicit Monte Carlo (SIMC) method and a comparison is made between the standard formulation and the difference formulation. The SIMC 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.

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PDF-file: 31 pages; size: 1 Mbytes

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  • Presented at: Computational Methods in Transport Workshop, Lake Tahoe, CA, United States, Sep 11 - Sep 16, 2004

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  • Report No.: UCRL-PROC-210979
  • Grant Number: W-7405-ENG-48
  • Office of Scientific & Technical Information Report Number: 918402
  • Archival Resource Key: ark:/67531/metadc886882

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  • March 30, 2005

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  • Sept. 22, 2016, 2:13 a.m.

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  • Dec. 2, 2016, 7:04 p.m.

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Szoke, A; Brooks, E D; McKinley, M & Daffin, F. Accurate and efficient radiation transport in optically thick media -- by means of the Symbolic Implicit Monte Carlo method in the difference formulation, article, March 30, 2005; Livermore, California. (digital.library.unt.edu/ark:/67531/metadc886882/: accessed November 22, 2017), University of North Texas Libraries, Digital Library, digital.library.unt.edu; crediting UNT Libraries Government Documents Department.