A semi-discrete central scheme for incompressible multiphase flow in porous media in several space dimensions

In this work we present a Godunov-type semi-discrete central scheme for systems of conservation laws which allows for spatial heterogeneity of the storage coefficient, say, the porosity field. This scheme is used in the composition of a sequential splitting algorithm for simulating incompressible multiphase flow within rigid porous media, with both permeability and porosity fields heterogeneous. The proposed methodology composes a fundamental block in the simulation of complex flows in porous media, where the compressibility effects may be included. Numerical tests are presented to illustrate the accuracy of the proposed method in problems that simulate immiscible three-phase flow in heterogeneous porous media in two and three space dimensions.