A sharp-interface interpretation of a continuous density model for homogenization of gravity-driven flow in porous media

We examine homogenization methods applied to sharp-interface and diffuse-interface models for gravity-driven flow in heterogeneous porous media. Our work specifically examines a matrix of models that includes (1) a variable media, diffuse-interface model, (2) a variable media, sharp-interface model, (3) a homogenized media, diffuse-interface model and (4) a homogenized media, sharp-interface model. We connect all four of these models via homogenization theory and sharp-interface limits. We show that existing results based on homogenization methods applied to sharp-interface models can be recovered by a less direct but more rigorous approach involving well-established homogenization theory and sharp-interface limits.