Superconvergence of a fully conservative finite difference method on non-uniform staggered grids for simulating wormhole propagation with the Darcy–Brinkman–Forchheimer framework

Abstract

In this paper, a finite difference scheme on non-uniform staggered grids is proposed for wormhole propagation with the Darcy–Brinkman–Forchheimer framework in porous media by introducing an auxiliary flux variable to guarantee full mass conservation. Error estimates for the pressure, velocity, porosity, concentration and auxiliary flux with second-order superconvergence in different discrete norms are established rigorously and carefully on non-uniform grids. We also obtain second-order superconvergence for some terms of the $H^{1}$ norm of the velocity on non-uniform grids. Finally, some numerical experiments are presented to verify the theoretical analysis and effectiveness of the proposed scheme.