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首页> 外文期刊>Journal of Computational Physics >Linearity preserving nine-point schemes for diffusion equation on distorted quadrilateral meshes
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Linearity preserving nine-point schemes for diffusion equation on distorted quadrilateral meshes

机译：变形四边形网格上扩散方程的保线性九点格式

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摘要

In this paper, we employ the so-called linearity preserving method, which requires that a difference scheme should be exact on linear solutions, to derive a nine-point difference scheme for the numerical solution of diffusion equation on the structured quadrilateral meshes. This scheme uses firstly both cell-centered unknowns and vertex unknowns, and then the vertex unknowns are treated as a linear combination of the surrounding cell-centered unknowns, which reduces the scheme to a cell-centered one. The weights in the linear combination are derived through the linearity preserving approach and can be obtained by solving a local linear system whose solvability is rigorously discussed. Moreover, the relations between our linearity preserving scheme and some existing schemes are also discussed, by which a generalized multipoint flux approximation scheme based on the linearity preserving criterion is suggested. Numerical experiments show that the linearity preserving schemes in this paper have nearly second order accuracy on many highly skewed and highly distorted structured quadrilateral meshes.
机译：在本文中，我们采用了所谓的线性保留方法，该方法要求在线性解上必须有一个精确的差分格式，从而为结构化四边形网格上的扩散方程的数值解导出一个九点差分格式。该方案首先使用以单元为中心的未知数和顶点未知数，然后将顶点未知数作为周围以单元为中心的未知数的线性组合，从而将该方案简化为以单元为中心的未知数。线性组合中的权重是通过线性保留方法得出的，可以通过求解局部线性系统来获得，该线性系统的可求解性经过严格讨论。此外，还讨论了线性保持方案与现有方案之间的关系，提出了一种基于线性保持准则的广义多点通量近似方案。数值实验表明，本文的线性保持方案在许多高度偏斜和高度变形的结构四边形网格上具有接近二阶的精度。

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