Year: 2023
Author: Wang Kong, Zhenying Hong, Guangwei Yuan, Zhiqiang Sheng
Advances in Applied Mathematics and Mechanics, Vol. 15 (2023), Iss. 2 : pp. 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.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/aamm.OA-2021-0280
Advances in Applied Mathematics and Mechanics, Vol. 15 (2023), Iss. 2 : pp. 402–427
Published online: 2023-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 26
Keywords: Extremum-preserving correction diffusion equation distorted mesh nine-point scheme.