A Variable Eddington Factor method for the 1-D grey radiative transfer equations with discontinuous Galerkin and mixed finite-element spatial differencing

Lou, Jijie; Morel, Jim E.; Gentile, N. A.

doi:10.1016/j.jcp.2019.05.012

Title: A Variable Eddington Factor method for the 1-D grey radiative transfer equations with discontinuous Galerkin and mixed finite-element spatial differencing

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Abstract

The purpose of this paper is to present a Variable Eddington Factor (VEF) method for the 1-D grey radiative transfer equations that uses a lumped linear discontinuous Galerkin spatial discretization for the Sequations together with a constant-linear mixed finite-element discretization for the VEF moment and material temperature equations. The use of independent discretizations can be particularly useful for multiphysics applications such as radiation-hydrodynamics. The VEF method is quite old, but to our knowledge, this particular combination of differencing schemes has not been previously investigated for radiative transfer. We define the scheme and present computational results. As expected, the scheme exhibits second-order accuracy for the directionally-integrated intensity and material temperature, and behaves well in the thick diffusion limit. An important focus of this study is the treatment of the strong temperature dependence of the opacities and the spatial dependence of the opacities within each cell, which are not explicitly defined by the basic discretization schemes.

Authors:

Lou, Jijie ^[1];

^[1]; Gentile, N. A. ^[2]

Texas A & M Univ., College Station, TX (United States). Dept. of Nuclear Engineering
Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)

Publication Date:: Sun Sep 01 00:00:00 EDT 2019

Research Org.:: Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)

Sponsoring Org.:: USDOE National Nuclear Security Administration (NNSA)

OSTI Identifier:: 1518563

Alternate Identifier(s):: OSTI ID: 1702383

Report Number(s):: LLNL-JRNL-759300
Journal ID: ISSN 0021-9991; 947531

Grant/Contract Number:: AC52-07NA27344

Resource Type:: Accepted Manuscript

Journal Name:: Journal of Computational Physics

Additional Journal Information:: Journal Volume: 393; Journal Issue: C; Journal ID: ISSN 0021-9991

Publisher:: Elsevier

Country of Publication:: United States

Language:: English

Subject:: 97 MATHEMATICS AND COMPUTING; 73 NUCLEAR PHYSICS AND RADIATION PHYSICS; Variable Eddington Factor; Quasi-diffusion; Discontinuous Galerkin; Mixed finite-element

Citation Formats


                    Lou, Jijie, Morel, Jim E., and Gentile, N. A. A Variable Eddington Factor method for the 1-D grey radiative transfer equations with discontinuous Galerkin and mixed finite-element spatial differencing.  United States: N. p., 2019. 
Web.  doi:10.1016/j.jcp.2019.05.012.

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                    Lou, Jijie, Morel, Jim E., & Gentile, N. A. A Variable Eddington Factor method for the 1-D grey radiative transfer equations with discontinuous Galerkin and mixed finite-element spatial differencing.  United States.  https://doi.org/10.1016/j.jcp.2019.05.012

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                    Lou, Jijie, Morel, Jim E., and Gentile, N. A. Sun .  
"A Variable Eddington Factor method for the 1-D grey radiative transfer equations with discontinuous Galerkin and mixed finite-element spatial differencing".  United States.  https://doi.org/10.1016/j.jcp.2019.05.012.  https://www.osti.gov/servlets/purl/1518563.

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@article{osti_1518563,

  title        = {A Variable Eddington Factor method for the 1-D grey radiative transfer equations with discontinuous Galerkin and mixed finite-element spatial differencing},

  author       = {Lou, Jijie and Morel, Jim E. and Gentile, N. A.},

  abstractNote = {The purpose of this paper is to present a Variable Eddington Factor (VEF) method for the 1-D grey radiative transfer equations that uses a lumped linear discontinuous Galerkin spatial discretization for the Sequations together with a constant-linear mixed finite-element discretization for the VEF moment and material temperature equations. The use of independent discretizations can be particularly useful for multiphysics applications such as radiation-hydrodynamics. The VEF method is quite old, but to our knowledge, this particular combination of differencing schemes has not been previously investigated for radiative transfer. We define the scheme and present computational results. As expected, the scheme exhibits second-order accuracy for the directionally-integrated intensity and material temperature, and behaves well in the thick diffusion limit. An important focus of this study is the treatment of the strong temperature dependence of the opacities and the spatial dependence of the opacities within each cell, which are not explicitly defined by the basic discretization schemes.},

  doi          = {10.1016/j.jcp.2019.05.012},

  journal      = {Journal of Computational Physics},

  number       = C,

  volume       = 393,

  place        = {United States},

  year         = {Sun Sep 01 00:00:00 EDT 2019},

  month        = {Sun Sep 01 00:00:00 EDT 2019}

}

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