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

Cheng Wang, Qiwei Sheng, Weimin Han

Type: Article

Publication Date: 2016-11-01

Citations: 4

DOI: https://doi.org/10.4208/cicp.310715.290316a

Abstract

Abstract 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.

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+	Theory of Differential Approximations of Radiative Transfer Equation	2013	Weimin Han Joseph Eichholz Qiwei Sheng
+	SOLUTION OF THE TRANSPORT EQUATION BY THE Sn METHOD	1958	B.G. Carlson George I. Bell
+	Boundary Value Problems for Transport Equations	1998	V. I. Agoshkov
+	Discrete-Ordinate Discontinuous Galerkin Methods for Solving the Radiative Transfer Equation	2010	Weimin Han Jianguo Huang Joseph Eichholz
+ PDF Chat	Analysis of a numerical solver for radiative transport equation	2012	Hao Gao Hongkai Zhao
+	A theoretical study for RTE-based parameter identification problems	2013	Jinping Tang Weimin Han Bo Han
+	An Introduction to Numerical Analysis	1990	F. S. Kendall Atkinson
+	Cubature over the sphere <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si1.gif" overflow="scroll"><mml:msup><mml:mrow><mml:mi>S</mml:mi></mml:mrow><mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:msup></mml:math> in Sobolev spaces of arbitrary order	2006	Kerstin Hesse Ian H. Sloan
+	Simulating radiative transfer with filtered spherical harmonics	2010	Ryan G. McClarren Cory D. Hauck
+	Inverse transport theory and applications	2009	Guillaume Bal