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Extremum-Preserving Correction of the Nine-Point Scheme for Diffusion Equation on Distorted Meshes

Extremum-Preserving Correction of the Nine-Point Scheme for Diffusion Equation on Distorted Meshes
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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.

Author Details

Wang Kong

Zhenying Hong

Guangwei Yuan

Zhiqiang Sheng

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    Sheng, Zhiqiang | Yuan, Guangwei

    Journal of Computational and Applied Mathematics, Vol. 436 (2024), Iss. P.115438

    https://doi.org/10.1016/j.cam.2023.115438 [Citations: 0]

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    Numerical Methods for Partial Differential Equations, Vol. 39 (2023), Iss. 6 P.4270

    https://doi.org/10.1002/num.23050 [Citations: 0]