A Finite Difference Scheme for Compressible Miscible Displacement Flow in Porous Media on Grids with Local Refinement in Time

Abstract

Considering two-dimensional compressible miscible displacement flow in porous media, finite difference schemes on grids with local refinement in time are constructed and studied. The construction utilizes a modified upwind approximation and linear interpolation at the slave nodes. Error analysis is presented in the maximum norm and numerical examples illustrating the theory are given.