A pyramid scheme for three-dimensional diffusion equations on polyhedral meshes

JOURNAL OF COMPUTATIONAL PHYSICS

卷:350

Article

Wang, Shuai^1,2  Hang, Xudeng¹  Yuan, Guangwei^1,2 

[1] Inst Appl Phys & Computat Math, Fenghaodong Rd, Beijing 100094, Peoples R China

[2] Lab Computat Phys, POB 8009, Beijing 100088, Peoples R China

关键词: Finite volume scheme;    Polyhedral cell with nonplanar faces;    3D diffusion equation;    The pyramid scheme;   

DOI  :  10.1016/j.jcp.2017.08.060

来源: Elsevier

【 摘 要 】

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. (C) 2017 Elsevier Inc. All rights reserved.

【 授权许可】

Free