Guangwei Yuan, Institute of Applied Physics and Computational Mathematics
601, Pao Yue-Kong Library
It is a challenging task to construct an accurate and efficient numerical scheme for three dimensional diffusion equations on distorted meshes. Many two-dimensional diffusion schemes cannot be directly extended to three dimensional case due to the complex geometry. In particular, nonplanar cell-face appears usually in polyhedral meshes. In this talk, some cell-centered finite volume schemes for three-dimensional diffusion equations on general polyhedral meshes are reviewed. Then some new finite volume schemes are presented, which are designed to be applicable for general polyhedral cells with nonplanar cell-faces. By introducing a so-called effective normal vector for cell-face, a simple expression is obtained for discrete normal flux even if it is on nonplanar cell-faces. Numerical results are given to show the performance of the new scheme on various kinds of distorted meshes.