A nonlinear finite volume scheme for diffusion equation on distorted meshes

Zhiqiang Sheng

Laboratory of Computational Physics,

Institute of Applied Physics and Computational Mathematics, Beijing.

Email: sheng_zhiqiang@iapcm.ac.cn

Abstract: In the construction of existing nonlinear cell-centered finite volume schemes preserving positivity, it is required to assume that values of auxiliary unknowns are nonnegative. However, this assumption is not always satisfied. In this talk, we present a new nonlinear finite volume scheme preserving positivity for diffusion equations on distorted meshes. The main feature of the scheme is the assumption that the values of auxiliary unknowns are nonnegative is avoided. Two nonnegative parameters are introduced to define a new nonlinear two-point flux, in which one point is the cell-center and the other is the midpoint of cell-edge. The final flux on the edge is obtained by the continuity of normal flux. Numerical results show that the accuracy of both solution and flux for our new scheme is superior to that of some existing schemes preserving positivity.