Review of interface methods for fluid computations

An interface method of computation is one which preserves as an exact identity the boundary between distinct computational regions, such as the interface between distinct fluids in a fluid flow problem. This article will motivate and review interface methods in the context of flow in porous media. The elimination of numerical diffusion is the major issue addressed by interface methods. Their natural role is in problems for which numerical mixing introduces significant scientific error. The study of the mixing process itself provides an example, since physically induced mixing must be clearly separated from numerically induced mixing in such a study. More generally, problems with important or computationally difficult interfaces or approximate discontinuities may benefit from the use of interface methods.