A positivity-preserving pyramid scheme for anisotropic diffusion problems on general hexahedral meshes with nonplanar cell faces

In this paper, a new cell-centered positivity-preserving pyramid scheme (called P3-scheme) is proposed for anisotropic diffusion problems. It can be regarded as a development of the O-scheme [31] for general hexahedral meshes with nonplanar cell-faces. In the P3-scheme, the flux on the nonplanar cell-face is approximated by the so called effective directional flux. Compared with the O-scheme, the P3-scheme is much more robust with respect to the distortion of the meshes, and has lower cost in computation and storage. Being different from the P-scheme [32], the P3-scheme is positivity-preserving and can be applied to anisotropic diffusion problems. Numerical results are presented to show the performance of P3-scheme on various kinds of distorted meshes for problems with continuous and discontinuous diffusion coefficients.