Volume 32, Issue 2
The Asymptotic Preserving Unified Gas Kinetic Scheme for Gray Radiative Transfer Equations on Distorted Quadrilateral Meshes

Wenjun Sun, Qinghong Zeng & Shanggui Li

Ann. Appl. Math., 32 (2016), pp. 141-165.

Published online: 2022-06

Export citation
  • 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.

  • AMS Subject Headings

82D05

  • Copyright

COPYRIGHT: © Global Science Press

  • Email address
  • BibTex
  • RIS
  • TXT
@Article{AAM-32-141, author = {Sun , WenjunZeng , Qinghong and Li , Shanggui}, title = {The Asymptotic Preserving Unified Gas Kinetic Scheme for Gray Radiative Transfer Equations on Distorted Quadrilateral Meshes}, journal = {Annals of Applied Mathematics}, year = {2022}, volume = {32}, number = {2}, pages = {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.

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

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.

Sun , WenjunZeng , Qinghong and Li , Shanggui. (2022). The Asymptotic Preserving Unified Gas Kinetic Scheme for Gray Radiative Transfer Equations on Distorted Quadrilateral Meshes. Annals of Applied Mathematics. 32 (2). 141-165. doi:
Copy to clipboard
The citation has been copied to your clipboard