Year: 2021
Author: Jianguo Huang, Yue Yu
Communications in Computational Physics, Vol. 30 (2021), Iss. 4 : pp. 1009–1036
Abstract
The radiative transfer equation is a fundamental equation in transport theory and applications, which is a 5-dimensional PDE in the stationary one-velocity case, leading to great difficulties in numerical simulation. To tackle this bottleneck, we first use the discrete ordinate technique to discretize the scattering term, an integral with respect to the angular variables, resulting in a semi-discrete hyperbolic system. Then, we make the spatial discretization by means of the discontinuous Galerkin (DG) method combined with the sparse grid method. The final linear system is solved by the block Gauss-Seidal iteration method. The computational complexity and error analysis are developed in detail, which show the new method is more efficient than the original discrete ordinate DG method. A series of numerical results are performed to validate the convergence behavior and effectiveness of the proposed method.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/cicp.OA-2020-0248
Communications in Computational Physics, Vol. 30 (2021), Iss. 4 : pp. 1009–1036
Published online: 2021-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 28
Keywords: Radiative transfer equation sparse grid method discrete ordinate method discontinuous Galerkin method.
Author Details
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A discrete-ordinate weak Galerkin method for radiative transfer equation
Singh, Maneesh Kumar
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https://doi.org/10.1016/j.apnum.2024.02.009 [Citations: 1]