Adaptive Dynamic Grids and Mimetic Finite Difference Method for Miscible Displacement Problem

We consider the solution of a two-phase miscible displacement problem on dynamic adaptive meshes using the mimetic finite difference method. The mimetic finite difference method is employed to discretize the Darcy law and the mass fraction advection-dispersion equation. We propose modifications to the mimetic finite difference method: to reproduce two-point flux approximation on \(\mathbb{K}\) -orthogonal grids and address degenerate advection-diffusion problems. We validate the method and demonstrate its applicability to the viscous fingering problem with adaptive mesh refinement.