Characteristic block-centered finite difference method for compressible miscible displacement in porous media

In this paper, the characteristic block-centered finite difference method is introduced and analyzed to solve compressible miscible displacement in porous media. Error estimates for the pressure, velocity, concentration and its flux in different discrete norms are established rigorously and carefully on non-uniform grids. Finally, some numerical experiments are presented to show that the convergence rates are in agreement with the theoretical analysis.