Uniform convergence of an upwind discontinuous Galerkin method for solving scaled discrete-ordinate radiative transfer equations with isotropic scattering

Sheng, Qiwei; Hauck, Cory D.

doi:10.1090/mcom/3670

Title: Uniform convergence of an upwind discontinuous Galerkin method for solving scaled discrete-ordinate radiative transfer equations with isotropic scattering

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Abstract

Here we present an error analysis for the discontinuous Galerkin (DG) method applied to the discrete-ordinate discretization of the steady-state radiative transfer equation with isotropic scattering. Under some mild assumptions, we show that the DG method converges uniformly with respect to a scaling parameter which characterizes the strength of scattering in the system. However, the rate is not optimal and can be polluted by the presence of boundary layers. In one-dimensional slab geometries, we demonstrate optimal convergence when boundary layers are not present and analyze a simple strategy for balance interior and boundary layer errors. Some numerical tests are also provided in this reduced setting.

Authors:

^[1];

^[2]

California State University, Bakersfield, CA (United States)
Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States)

Publication Date:: Mon Jul 19 00:00:00 EDT 2021

Research Org.:: Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States)

Sponsoring Org.:: USDOE Office of Science (SC), Advanced Scientific Computing Research (ASCR); National Science Foundation (NSF)

OSTI Identifier:: 1838952

Grant/Contract Number:: AC05-00OR22725; 1217170

Resource Type:: Accepted Manuscript

Journal Name:: Mathematics of Computation

Additional Journal Information:: Journal Volume: 90; Journal Issue: 332; Journal ID: ISSN 0025-5718

Publisher:: American Mathematical Society

Country of Publication:: United States

Language:: English

Subject:: 97 MATHEMATICS AND COMPUTING

Citation Formats


                    Sheng, Qiwei, and Hauck, Cory D. Uniform convergence of an upwind discontinuous Galerkin method for solving scaled discrete-ordinate radiative transfer equations with isotropic scattering.  United States: N. p., 2021. 
Web.  doi:10.1090/mcom/3670.

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                    Sheng, Qiwei, & Hauck, Cory D. Uniform convergence of an upwind discontinuous Galerkin method for solving scaled discrete-ordinate radiative transfer equations with isotropic scattering.  United States.  https://doi.org/10.1090/mcom/3670

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                    Sheng, Qiwei, and Hauck, Cory D. Mon .  
"Uniform convergence of an upwind discontinuous Galerkin method for solving scaled discrete-ordinate radiative transfer equations with isotropic scattering".  United States.  https://doi.org/10.1090/mcom/3670.  https://www.osti.gov/servlets/purl/1838952.

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@article{osti_1838952,

  title        = {Uniform convergence of an upwind discontinuous Galerkin method for solving scaled discrete-ordinate radiative transfer equations with isotropic scattering},

  author       = {Sheng, Qiwei and Hauck, Cory D.},

  abstractNote = {Here we present an error analysis for the discontinuous Galerkin (DG) method applied to the discrete-ordinate discretization of the steady-state radiative transfer equation with isotropic scattering. Under some mild assumptions, we show that the DG method converges uniformly with respect to a scaling parameter which characterizes the strength of scattering in the system. However, the rate is not optimal and can be polluted by the presence of boundary layers. In one-dimensional slab geometries, we demonstrate optimal convergence when boundary layers are not present and analyze a simple strategy for balance interior and boundary layer errors. Some numerical tests are also provided in this reduced setting.},

  doi          = {10.1090/mcom/3670},

  journal      = {Mathematics of Computation},

  number       = 332,

  volume       = 90,

  place        = {United States},

  year         = {Mon Jul 19 00:00:00 EDT 2021},

  month        = {Mon Jul 19 00:00:00 EDT 2021}

}

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