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DOI码：10.4208/jcm.2303-m2022-0139
所属单位：数学学院
发表刊物：Journal of Computational Mathematics
关键字：Monotonicity corrections, Diffusion equation, Improved MPFA, Distorted meshes
摘要：In this paper, we present a nonlinear correction technique to modify the nine-point scheme proposed in [SIAM J. Sci. Comput., 30:3 (2008), 1341–1361] such that the resulted scheme preserves the positivity. We first express the flux by the cell-centered unknowns and edge unknowns based on the stencil of the nine-point scheme. Then, we use a nonlinear combination technique to get a monotone scheme. In order to obtain a cell-centered finite volume scheme, we need to use the cell-centered unknowns to locally approximate the auxiliary unknowns. We present a new method to approximate the auxiliary unknowns by using the idea of an improved multi-points flux approximation. The numerical results show that the new proposed scheme is robust, can handle some distorted grids that some existing finite volume schemes could not handle, and has higher numerical accuracy than some existing positivity-preserving finite volume schemes.
论文类型：期刊论文
学科门类：理学
文献类型：J
卷号：2024
期号：42
页面范围：1277-1304
是否译文：否
发表时间：2024-07-18
收录刊物：SCI
合写作者：洪振英,袁光伟
通讯作者：盛志强

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