Ray Effect Mitigation for the Discrete Ordinates Method Using Artificial Scattering

Martin Frank; Jonas Kusch; Thomas Camminady; Cory D. Hauck

doi:10.1080/00295639.2020.1730665

Ray Effect Mitigation for the Discrete Ordinates Method Using Artificial Scattering

Martin Frank, Jonas Kusch, Thomas Camminady, Cory D. Hauck

Multiscale Methods

Research output: Contribution to journal › Article › peer-review

12 Scopus citations

Abstract

Solving the radiative transfer equation with the discrete ordinates (S (Formula presented.)) method leads to a nonphysical imprint of the chosen quadrature set on the solution. To mitigate these so-called ray effects, we propose a modification of the S (Formula presented.) method that we call artificial scattering S (Formula presented.) (as-S (Formula presented.)). The method adds an artificial forward-peaked scattering operator that generates angular diffusion to the solution and thereby mitigates ray effects. Similar to artificial viscosity for spatial discretizations, the additional term vanishes as the number of ordinates approaches infinity. Our method allows an efficient implementation of explicit and implicit time integration according to standard S (Formula presented.) solver technology. For two test cases, we demonstrate a significant reduction of error for the as-S (Formula presented.) method when compared to the standard S (Formula presented.) method, both for explicit and implicit computations. Furthermore, we show that a prescribed numerical precision can be reached with less memory due to the reduction in the number of ordinates.

Original language	English
Pages (from-to)	971-988
Number of pages	18
Journal	Nuclear Science and Engineering
Volume	194
Issue number	11
DOIs	https://doi.org/10.1080/00295639.2020.1730665
State	Published - Nov 1 2020

Funding

This material is based upon work supported by the National Science Foundation under Grant No. 1913277 and by UT-Battelle, LLC, under Contract No. DE-AC0500OR22725 with the U.S. Department of Energy. The United States Government retains and the publisher, by accepting the article for publication, acknowledges that the United States Government retains a non-exclusive, paid-up, irrevocable, world-wide license to publish or reproduce the published form of this manuscript, or allow others to do so, for the United States Government purposes. The Department of Energy will provide public access to these results of federally sponsored research in accordance with the DOE Public Access Plan ( http://energy.gov/downloads/doe-public-access-plan ). The authors wish to thank Ryan G. McClarren (University of Notre Dame) for many fruitful discussions. This material is based upon work supported by the National Science Foundation under Grant No. 1913277 and by UT-Battelle, LLC, under Contract No. DE-AC0500OR22725 with the U.S. Department of Energy. The United States Government retains and the publisher, by accepting the article for publication, acknowledges that the United States Government retains a non-exclusive, paid-up, irrevocable, world-wide license to publish or reproduce the published form of this manuscript, or allow others to do so, for the United States Government purposes. The Department of Energy will provide public access to these results of federally sponsored research in accordance with the DOE Public Access Plan (http://energy.gov/downloads/doe-public-access-plan).

Funders	Funder number
DOE Public Access Plan
UT-Battelle, LLC	DE-AC0500OR22725
United States Government
National Science Foundation	1913277
U.S. Department of Energy

Keywords

Discrete ordinates method
radiative transfer, quadrature
ray effects

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10.1080/00295639.2020.1730665

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title = "Ray Effect Mitigation for the Discrete Ordinates Method Using Artificial Scattering",

abstract = "Solving the radiative transfer equation with the discrete ordinates (S (Formula presented.)) method leads to a nonphysical imprint of the chosen quadrature set on the solution. To mitigate these so-called ray effects, we propose a modification of the S (Formula presented.) method that we call artificial scattering S (Formula presented.) (as-S (Formula presented.)). The method adds an artificial forward-peaked scattering operator that generates angular diffusion to the solution and thereby mitigates ray effects. Similar to artificial viscosity for spatial discretizations, the additional term vanishes as the number of ordinates approaches infinity. Our method allows an efficient implementation of explicit and implicit time integration according to standard S (Formula presented.) solver technology. For two test cases, we demonstrate a significant reduction of error for the as-S (Formula presented.) method when compared to the standard S (Formula presented.) method, both for explicit and implicit computations. Furthermore, we show that a prescribed numerical precision can be reached with less memory due to the reduction in the number of ordinates.",

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AU - Hauck, Cory D.

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Y1 - 2020/11/1

N2 - Solving the radiative transfer equation with the discrete ordinates (S (Formula presented.)) method leads to a nonphysical imprint of the chosen quadrature set on the solution. To mitigate these so-called ray effects, we propose a modification of the S (Formula presented.) method that we call artificial scattering S (Formula presented.) (as-S (Formula presented.)). The method adds an artificial forward-peaked scattering operator that generates angular diffusion to the solution and thereby mitigates ray effects. Similar to artificial viscosity for spatial discretizations, the additional term vanishes as the number of ordinates approaches infinity. Our method allows an efficient implementation of explicit and implicit time integration according to standard S (Formula presented.) solver technology. For two test cases, we demonstrate a significant reduction of error for the as-S (Formula presented.) method when compared to the standard S (Formula presented.) method, both for explicit and implicit computations. Furthermore, we show that a prescribed numerical precision can be reached with less memory due to the reduction in the number of ordinates.

AB - Solving the radiative transfer equation with the discrete ordinates (S (Formula presented.)) method leads to a nonphysical imprint of the chosen quadrature set on the solution. To mitigate these so-called ray effects, we propose a modification of the S (Formula presented.) method that we call artificial scattering S (Formula presented.) (as-S (Formula presented.)). The method adds an artificial forward-peaked scattering operator that generates angular diffusion to the solution and thereby mitigates ray effects. Similar to artificial viscosity for spatial discretizations, the additional term vanishes as the number of ordinates approaches infinity. Our method allows an efficient implementation of explicit and implicit time integration according to standard S (Formula presented.) solver technology. For two test cases, we demonstrate a significant reduction of error for the as-S (Formula presented.) method when compared to the standard S (Formula presented.) method, both for explicit and implicit computations. Furthermore, we show that a prescribed numerical precision can be reached with less memory due to the reduction in the number of ordinates.

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Ray Effect Mitigation for the Discrete Ordinates Method Using Artificial Scattering

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