A pyramid scheme for three-dimensional diffusion equations on polyhedral meshes
A pyramid scheme for three-dimensional diffusion equations on polyhedral meshes
复制标题
多面体网格上三维扩散方程的金字塔方案
DOI：
10.1016/j.jcp.2017.08.060
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发表时间：
2017
影响因子：
4.1
通讯作者：
Yuan Guangwei
中科院分区：
文献类型：
--
作者：
Wang Shuai;Hang Xudeng;Yuan Guangwei
本文对三维扩散方程在多面体网格上提出了一种新的中心网格有限体积格式，称为金字塔格式（P-格式）。该方案是为具有非平面单元面的多面体单元而设计的。将非平面网格面上的法向通量离散到平面网格上，并通过简单的优化方法确定网格面上的法向通量。由此得到的法向通量的离散形式只涉及胞心和胞顶点未知数，而不涉及面心未知数。在六面体网格具有倾斜非平面网格面的情况下，得到了一个相当简单的离散法向通量的表达式。与二阶精度的O格式[31]相比，P格式具有更好的鲁棒性，且离散化代价显著降低。数值结果显示了P格式在各种变形网格上的性能。特别是，P-方案被证明具有二阶精度。
In this paper, a new cell-centered finite volume scheme is proposed for three-dimensional diffusion equations on polyhedral meshes, which is called as pyramid scheme (P-scheme). The scheme is designed for polyhedral cells with nonplanar cell-faces. The normal flux on a nonplanar cell-face is discretized on a planar face, which is determined by a simple optimization procedure. The resulted discrete form of the normal flux involves only cell-centered and cell-vertex unknowns, and is free from face-centered unknowns. In the case of hexahedral meshes with skewed nonplanar cell-faces, a quite simple expression is obtained for the discrete normal flux. Compared with the second order accurate O-scheme [31], the P-scheme is more robust and the discretization cost is reduced remarkably. Numerical results are presented to show the performance of the P-scheme on various kinds of distorted meshes. In particular, the P-scheme is shown to be second order accurate.