The Asymptotic Preserving Unified Gas Kinetic Scheme for Gray Radiative Transfer Equations on Distorted Quadrilateral Meshes
Year: 2016
Author: Wenjun Sun, Qinghong Zeng, Shanggui Li
Annals of Applied Mathematics, Vol. 32 (2016), Iss. 2 : pp. 141–165
Abstract
In this paper, we consider the multi-dimensional asymptotic preserving unified gas kinetic scheme for gray radiative transfer equations on distorted quadrilateral meshes. Different from the former scheme [J. Comput. Phys. 285(2015), 265-279] on uniform meshes, in this paper, in order to obtain the boundary fluxes based on the framework of unified gas kinetic scheme (UGKS), we use the real multi-dimensional reconstruction for the initial data and the macro-terms in the equation of the gray transfer equations. We can prove that the scheme is asymptotic preserving, and especially for the distorted quadrilateral meshes, a nine-point scheme [SIAM J. SCI. COMPUT. 30(2008), 1341-1361] for the diffusion limit equations is obtained, which is naturally reduced to standard five-point scheme for the orthogonal meshes. The numerical examples on distorted meshes are included to validate the current approach.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/2016-AAM-20634
Annals of Applied Mathematics, Vol. 32 (2016), Iss. 2 : pp. 141–165
Published online: 2016-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 25
Keywords: gray radiative transfer equations distorted quadrilateral meshes asymptotic preserving unified gas kinetic scheme nine-point diffusion scheme.