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.
"A Finite Difference Scheme for Compressible Miscible Displacement Flow in Porous Media on Grids with Local Refinement in Time." Abstr. Appl. Anal. 2013 (SI17) 1 - 8, 2013. https://doi.org/10.1155/2013/521835