A fully conservative block-centered finite difference method for Darcy-Forchheimer incompressible miscible displacement problem

In this paper, a block-centered finite difference method is derived for the Darcy-Forchheimer incompressible miscible displacement problem in porous media by introducing an auxiliary flux variable to guarantee full mass conservation. Error estimates for the pressure, velocity, concentration, and auxiliary flux in different discrete norms are established rigorously and carefully on nonuniform grids. Finally, some numerical experiments are presented to show that the convergence rates are in agreement with the theoretical analysis.