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Volume 30, Issue 2
An Efficient Positivity-Preserving Finite Volume Scheme for the Nonequilibrium Three-Temperature Radiation Diffusion Equations on Polygonal Meshes

Shuai Su, Huazhong Tang & Jiming Wu

Commun. Comput. Phys., 30 (2021), pp. 448-485.

Published online: 2021-05

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  • Abstract

This paper develops an efficient positivity-preserving finite volume scheme for the two-dimensional nonequilibrium three-temperature radiation diffusion equations on general polygonal meshes. The scheme is formed as a predictor-corrector algorithm. The corrector phase obtains the cell-centered solutions on the primary mesh, while the predictor phase determines the cell-vertex solutions on the dual mesh independently. Moreover, the flux on the primary edge is approximated with a fixed stencil and the nonnegative cell-vertex solutions are not reconstructed. Theoretically, our scheme does not require any nonlinear iteration for the linear problems, and can call the fast nonlinear solver (e.g. Newton method) for the nonlinear problems. The positivity, existence and uniqueness of the cell-centered solutions obtained on the corrector phase are analyzed, and the scheme on quasi-uniform meshes is proved to be $L^2$- and $H^1$-stable under some assumptions. Numerical experiments demonstrate the accuracy, efficiency and positivity of the scheme on various distorted meshes.

  • AMS Subject Headings

65M08, 65M22

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{CiCP-30-448, author = {Su , ShuaiTang , Huazhong and Wu , Jiming}, title = {An Efficient Positivity-Preserving Finite Volume Scheme for the Nonequilibrium Three-Temperature Radiation Diffusion Equations on Polygonal Meshes}, journal = {Communications in Computational Physics}, year = {2021}, volume = {30}, number = {2}, pages = {448--485}, abstract = {

This paper develops an efficient positivity-preserving finite volume scheme for the two-dimensional nonequilibrium three-temperature radiation diffusion equations on general polygonal meshes. The scheme is formed as a predictor-corrector algorithm. The corrector phase obtains the cell-centered solutions on the primary mesh, while the predictor phase determines the cell-vertex solutions on the dual mesh independently. Moreover, the flux on the primary edge is approximated with a fixed stencil and the nonnegative cell-vertex solutions are not reconstructed. Theoretically, our scheme does not require any nonlinear iteration for the linear problems, and can call the fast nonlinear solver (e.g. Newton method) for the nonlinear problems. The positivity, existence and uniqueness of the cell-centered solutions obtained on the corrector phase are analyzed, and the scheme on quasi-uniform meshes is proved to be $L^2$- and $H^1$-stable under some assumptions. Numerical experiments demonstrate the accuracy, efficiency and positivity of the scheme on various distorted meshes.

}, issn = {1991-7120}, doi = {https://doi.org/10.4208/cicp.OA-2020-0088}, url = {http://global-sci.org/intro/article_detail/cicp/19121.html} }
TY - JOUR T1 - An Efficient Positivity-Preserving Finite Volume Scheme for the Nonequilibrium Three-Temperature Radiation Diffusion Equations on Polygonal Meshes AU - Su , Shuai AU - Tang , Huazhong AU - Wu , Jiming JO - Communications in Computational Physics VL - 2 SP - 448 EP - 485 PY - 2021 DA - 2021/05 SN - 30 DO - http://doi.org/10.4208/cicp.OA-2020-0088 UR - https://global-sci.org/intro/article_detail/cicp/19121.html KW - Radiation diffusion equations, positivity-preserving, high efficiency, stability, finite volume method. AB -

This paper develops an efficient positivity-preserving finite volume scheme for the two-dimensional nonequilibrium three-temperature radiation diffusion equations on general polygonal meshes. The scheme is formed as a predictor-corrector algorithm. The corrector phase obtains the cell-centered solutions on the primary mesh, while the predictor phase determines the cell-vertex solutions on the dual mesh independently. Moreover, the flux on the primary edge is approximated with a fixed stencil and the nonnegative cell-vertex solutions are not reconstructed. Theoretically, our scheme does not require any nonlinear iteration for the linear problems, and can call the fast nonlinear solver (e.g. Newton method) for the nonlinear problems. The positivity, existence and uniqueness of the cell-centered solutions obtained on the corrector phase are analyzed, and the scheme on quasi-uniform meshes is proved to be $L^2$- and $H^1$-stable under some assumptions. Numerical experiments demonstrate the accuracy, efficiency and positivity of the scheme on various distorted meshes.

Shuai Su, Huazhong Tang & Jiming Wu. (2021). An Efficient Positivity-Preserving Finite Volume Scheme for the Nonequilibrium Three-Temperature Radiation Diffusion Equations on Polygonal Meshes. Communications in Computational Physics. 30 (2). 448-485. doi:10.4208/cicp.OA-2020-0088
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