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Volume 15, Issue 2
Extremum-Preserving Correction of the Nine-Point Scheme for Diffusion Equation on Distorted Meshes

Wang Kong, Zhenying Hong, Guangwei Yuan & Zhiqiang Sheng

Adv. Appl. Math. Mech., 15 (2023), pp. 402-427.

Published online: 2022-12

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  • Abstract

In this paper, we construct a new cell-centered nonlinear finite volume scheme that preserves the extremum principle for heterogeneous anisotropic diffusion equation on distorted meshes. We introduce a new nonlinear approach to construct the conservative flux, that is, a linear second order flux is firstly given and a nonlinear conservative flux is then constructed by using an adaptive method and a nonlinear weighted method. Our new scheme does not need to use the convex combination of the cell-center unknowns to approximate the auxiliary unknowns, so it can deal with the problem with general discontinuous coefficients. Numerical results show that our new scheme performs more robust than some existing schemes on highly distorted meshes.

  • AMS Subject Headings

65N08, 65M08

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{AAMM-15-402, author = {Kong , WangHong , ZhenyingYuan , Guangwei and Sheng , Zhiqiang}, title = {Extremum-Preserving Correction of the Nine-Point Scheme for Diffusion Equation on Distorted Meshes}, journal = {Advances in Applied Mathematics and Mechanics}, year = {2022}, volume = {15}, number = {2}, pages = {402--427}, abstract = {

In this paper, we construct a new cell-centered nonlinear finite volume scheme that preserves the extremum principle for heterogeneous anisotropic diffusion equation on distorted meshes. We introduce a new nonlinear approach to construct the conservative flux, that is, a linear second order flux is firstly given and a nonlinear conservative flux is then constructed by using an adaptive method and a nonlinear weighted method. Our new scheme does not need to use the convex combination of the cell-center unknowns to approximate the auxiliary unknowns, so it can deal with the problem with general discontinuous coefficients. Numerical results show that our new scheme performs more robust than some existing schemes on highly distorted meshes.

}, issn = {2075-1354}, doi = {https://doi.org/10.4208/aamm.OA-2021-0280}, url = {http://global-sci.org/intro/article_detail/aamm/21274.html} }
TY - JOUR T1 - Extremum-Preserving Correction of the Nine-Point Scheme for Diffusion Equation on Distorted Meshes AU - Kong , Wang AU - Hong , Zhenying AU - Yuan , Guangwei AU - Sheng , Zhiqiang JO - Advances in Applied Mathematics and Mechanics VL - 2 SP - 402 EP - 427 PY - 2022 DA - 2022/12 SN - 15 DO - http://doi.org/10.4208/aamm.OA-2021-0280 UR - https://global-sci.org/intro/article_detail/aamm/21274.html KW - Extremum-preserving correction, diffusion equation, distorted mesh, nine-point scheme. AB -

In this paper, we construct a new cell-centered nonlinear finite volume scheme that preserves the extremum principle for heterogeneous anisotropic diffusion equation on distorted meshes. We introduce a new nonlinear approach to construct the conservative flux, that is, a linear second order flux is firstly given and a nonlinear conservative flux is then constructed by using an adaptive method and a nonlinear weighted method. Our new scheme does not need to use the convex combination of the cell-center unknowns to approximate the auxiliary unknowns, so it can deal with the problem with general discontinuous coefficients. Numerical results show that our new scheme performs more robust than some existing schemes on highly distorted meshes.

Wang Kong, Zhenying Hong, Guangwei Yuan & Zhiqiang Sheng. (2022). Extremum-Preserving Correction of the Nine-Point Scheme for Diffusion Equation on Distorted Meshes. Advances in Applied Mathematics and Mechanics. 15 (2). 402-427. doi:10.4208/aamm.OA-2021-0280
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