An extremum-preserving finite volume scheme for convection-diffusion equation on general meshes
An extremum-preserving finite volume scheme for convection-diffusion equation on general meshes
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DOI：
10.1016/j.amc.2020.125301
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发表时间：
2020-09
期刊：
影响因子：
--
通讯作者：
Gang Peng;Zhiming Gao;Xinlong Feng
中科院分区：
文献类型：
--
作者：
Gang Peng;Zhiming Gao;Xinlong Feng
本文给出了一般网格上对流扩散方程的保极值有限体积格式。利用非均质界面处的谐波平均点来定义辅助未知数。采用带坡度限制器的二阶迎风法对对流通量进行离散化。该方案只有以细胞为中心的未知数，并且拥有一个小模板。用标准假设证明了该格式的保极值性。数值结果表明，保持极值格式是求解变形网格上对流扩散方程的一种有效方法。
We present an extremum-preserving finite volume scheme for the convection-diffusion equation on general meshes in this article. The harmonic averaging point locating at the interface of heterogeneity are utilized to define the auxiliary unknowns. The second-order upwind method with a slope limiter is used for the discretization of convection flux. This scheme has only cell-centered unknowns and possesses a small stencil. The extremum-preserving property of this scheme is proved by standard assumption. Numerical results demonstrate that the extremum-preserving scheme is an efficient method in solving the convection-diffusion equation on distorted meshes.