Angularly Adaptive P1--Double P0 Diffusion Solutions of Non-Equilibrium Grey Radiative Transfer Problems in Planar Geometry

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The double spherical harmonics angular approximation in the lowest order, i.e. double P{sub 0} (DP{sub 0}), is developed for the solution of time-dependent non-equilibrium grey radiative transfer problems in planar geometry. The standard P{sub 1} angular approximation represents the angular dependence of the radiation specific intensity using a linear function in the angular domain -1 {le} {mu} {le} 1. In contrast, the DP{sub 0} angular approximation represents the angular dependence as isotropic in each half angular range -1 {le} {mu} < 0 and 0 < {mu} {le} 1. Neglecting the time derivative of the radiation flux, both the P{sub 1} ... continued below

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Brantley, P S June 6, 2005.

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The double spherical harmonics angular approximation in the lowest order, i.e. double P{sub 0} (DP{sub 0}), is developed for the solution of time-dependent non-equilibrium grey radiative transfer problems in planar geometry. The standard P{sub 1} angular approximation represents the angular dependence of the radiation specific intensity using a linear function in the angular domain -1 {le} {mu} {le} 1. In contrast, the DP{sub 0} angular approximation represents the angular dependence as isotropic in each half angular range -1 {le} {mu} < 0 and 0 < {mu} {le} 1. Neglecting the time derivative of the radiation flux, both the P{sub 1} and DP{sub 0} equations can be written as a single diffusion equation for the radiation energy density. Although the DP{sub 0} diffusion approximation is expected to be less accurate than the P{sub 1} diffusion approximation at and near thermodynamic equilibrium, the DP{sub 0} angular approximation can more accurately capture the complicated angular dependence near the non-equilibrium wave front. We develop an adaptive angular technique that locally uses either the DP{sub 0} or the P{sub 1} diffusion approximation depending on the degree to which the radiation and material fields are in thermodynamic equilibrium. Numerical results are presented for a test problem due to Su and Olson for which a semi-analytic transport solution exists. The numerical results demonstrate that the adaptive P{sub 1}-DP{sub 0} diffusion approximation can yield improvements in accuracy over the standard P{sub 1} diffusion approximation for non-equilibrium grey radiative transfer.

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PDF-file: 15 pages; size: 0.4 Mbytes

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  • Presented at: International Topical Meeting on Mathematics and Computation, Supercomputing, Reactor Physics and Nuclear and Biological Applications, Avignon, France, Sep 12 - Sep 15, 2005

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  • Report No.: UCRL-CONF-212750
  • Grant Number: W-7405-ENG-48
  • Office of Scientific & Technical Information Report Number: 878230
  • Archival Resource Key: ark:/67531/metadc880309

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  • June 6, 2005

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  • Sept. 21, 2016, 2:29 a.m.

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  • Nov. 22, 2016, 6:31 p.m.

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Brantley, P S. Angularly Adaptive P1--Double P0 Diffusion Solutions of Non-Equilibrium Grey Radiative Transfer Problems in Planar Geometry, article, June 6, 2005; Livermore, California. (digital.library.unt.edu/ark:/67531/metadc880309/: accessed August 17, 2017), University of North Texas Libraries, Digital Library, digital.library.unt.edu; crediting UNT Libraries Government Documents Department.