| Abstract: | In this paper, we suggest a new vertex interpolation algorithm to improvean existing cell-centered finite volume scheme for nonlinear diffusion problems ongeneral meshes. The new vertex interpolation algorithm is derived by applying a special limit procedure to the well-known MPFA-O method. Since the MPFA-O methodfor 3D cases has been addressed in some studies, the new vertex interpolation algorithm can be extended to 3D cases naturally. More interesting is that the solvabilityof the corresponding local system is proved under some assumptions. Additionally,we modify the edge flux approximation by an edge-based discretization of diffusion coefficient, and thus the improved scheme is free of the so-called numericalheat-barrier issue suffered by many existing cell-centered or hybrid schemes. Thefinal scheme allows arbitrary continuous or discontinuous diffusion coefficients andcan be applicable to arbitrary star-shaped polygonal meshes. A second-order convergence rate for the approximate solution and a first-order accuracy for the fluxare observed in numerical experiments. In the comparative experiments with someexisting vertex interpolation algorithms, the new algorithm shows obvious improvement on highly distorted meshes. |
