Exponential finite difference scheme for transport equations with discontinuous coefficients in porous media

摘要

In this paper, we propose a novel exponential difference scheme for solving non-linear problems arising in variably saturated flow with discontinuous absolute permeability. First, we derive the discretization for a linear convection-diffusion-reaction problem with discontinuous coefficients. Positivity preserving property, stability and convergence of the scheme are studied. Then, the method is implemented to the transport equation and Richards’ equation. Various numerical experiments on graded and uniform meshes are presented and discussed.