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A Discrete-Ordinate Discontinuous-Streamline Diffusion Method for the Radiative Transfer Equation

Part of: Partial differential equations, boundary value problems Integral equations, integral transforms

Published online by Cambridge University Press:  02 November 2016

Cheng Wang ,
Qiwei Sheng  and
Weimin Han
Cheng Wang*
Affiliation:
School of Mathematical Sciences, Tongji University, Shanghai 200092, China
Qiwei Sheng*
Affiliation:
Department of Mathematics, California State University, Bakersfield, CA 93311, USA
Weimin Han*
Affiliation:
Department of Mathematics, University of Iowa, Iowa City, IA 52242, USA
*
*Corresponding author. Email addresses:qsheng@csub.edu (Q. Sheng), wangcheng@tongji.edu.cn (C. Wang), weimin-han@uiowa.edu (W. Han)
*Corresponding author. Email addresses:qsheng@csub.edu (Q. Sheng), wangcheng@tongji.edu.cn (C. Wang), weimin-han@uiowa.edu (W. Han)
*Corresponding author. Email addresses:qsheng@csub.edu (Q. Sheng), wangcheng@tongji.edu.cn (C. Wang), weimin-han@uiowa.edu (W. Han)

Abstract

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The radiative transfer equation (RTE) arises in many different areas of science and engineering. In this paper, we propose and investigate a discrete-ordinate discontinuous-streamline diffusion (DODSD) method for solving the RTE, which is a combination of the discrete-ordinate technique and the discontinuous-streamline diffusion method. Different from the discrete-ordinate discontinuous Galerkin (DODG) method for the RTE, an artificial diffusion parameter is added to the test functions in the spatial discretization. Stability and error estimates in certain norms are proved. Numerical results show that the proposed method can lead to a more accurate approximation in comparison with the DODG method.

Keywords

Radiative transfer equationdiscrete-ordinate methoddiscontinuous-streamline diffusion methodstabilityerror estimation

MSC classification

Secondary: 65N30: Finite elements, Rayleigh-Ritz and Galerkin methods, finite methods 65R20: Integral equations

Information

Type
Research Article
Information
Communications in Computational Physics , Volume 20 , Issue 5 , November 2016 , pp. 1443 - 1465
Copyright
Copyright © Global-Science Press 2016 

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