Generalized Lagrangian coordinates for transport and two-phase flows in heterogeneous anisotropic porous media

We show how Lagrangian coordinates provide an effective representation of h ow difficult non-linear, hyperbolic transport problems in porous media can be dealt with. Recalling Lagrangian description first, we then derive some basic but remarkable properties useful for the numerical computation of pro jected transport operators. We furthermore introduce new generalized Lagran gian coordinates with their application to the Darcy-Muskat two-phase flow models. We show how these generalized Lagrangian coordinates can be constru cted from the global mass conservation, and that they are related to the ex istence of a global pressure previously defined in the literature about the subject. The whole representation is developed in two or three dimensions for numerical purposes, for isotropic or anisotropic heterogeneous porous m edia.