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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.
}, issn = {}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/aam/20634.html} }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.