The finite volume scheme preserving maximum principle for two-dimensional time-fractional Fokker–Planck equations on distorted meshes

Abstract

In this paper, we develop a nonlinear finite volume scheme preserving maximum principle for 2D time fractional Fokker–Planck equations on distorted meshes. The characteristic of our method is that it satisfies the discrete maximum principle such that it keeps physical boundedness such as concentration, temperature and density, etc. The analysis is based on an adaptive approach of choosing stencil to construct a maximum-principle-preserving discrete normal flux for diffusive flux. For the advection term, we use the second-order upwind method with proper slope limiter. The fractional derivative is approximated through L1-scheme. The advantages of our scheme are that it is locally conservative and can be applied to distorted meshes with no severe constraint on the time step. Numerical results verify the theoretical result and show that our scheme can preserve discrete maximum principle.