TY - JOUR
T1 - The Asymptotic Preserving Unified Gas Kinetic Scheme for Gray Radiative Transfer Equations on Distorted Quadrilateral Meshes
AU - Sun , Wenjun
AU - Zeng , Qinghong
AU - Li , Shanggui
JO - Annals of Applied Mathematics
VL - 2
SP - 141
EP - 165
PY - 2022
DA - 2022/06
SN - 32
DO - http://doi.org/
UR - https://global-sci.org/intro/article_detail/aam/20634.html
KW - gray radiative transfer equations, distorted quadrilateral meshes, asymptotic preserving, unified gas kinetic scheme, nine-point diffusion scheme.
AB - <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>