@Article{AAM-32-2,
author = {Wenjun, Sun and Zeng, Qinghong and Shanggui, Li},
title = {The Asymptotic Preserving Unified Gas Kinetic Scheme for Gray Radiative Transfer Equations on Distorted Quadrilateral Meshes},
journal = {Annals of Applied Mathematics},
year = {2016},
volume = {32},
number = {2},
pages = {141--165},
abstract = {<p style="text-align: justify;">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.</p>},
issn = {},
doi = {https://doi.org/2016-AAM-20634},
url = {https://global-sci.com/article/72778/the-asymptotic-preserving-unified-gas-kinetic-scheme-for-gray-radiative-transfer-equations-on-distorted-quadrilateral-meshes}
}