Monotone Finite Volume Schemes for Diffusion Equation with Imperfect Interface on Distorted Meshes

Abstract

In this paper, we prove the solution of diffusion equation with imperfect interface is positivity-preserving and a monotone finite volume method is presented to obtain the nonnegative solution on distorted mesh. Motivated by Sheng and Yuan (J Comput Phys 231:3739–3754, 2012), the discrete normal flux on interface is defined by using an extended stencil and introducing two auxiliary points to distinguish the discontinuities of the unknowns on both sides of the interface. The resulting finite volume scheme is locally conservative and has only cell-centered unknowns. Moreover, it is proved to be monotone. The numerical results show that the method obtains second order convergent rate in \(L_2\) norms for solutions on quadrilateral and triangular meshes.