A Sparse Grid Discrete Ordinate Discontinuous Galerkin Method for the Radiative Transfer Equation

A Sparse Grid Discrete Ordinate Discontinuous Galerkin Method for the Radiative Transfer Equation

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

Jianguo Huang

Yue Yu

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