A semi-discrete central scheme for the approximation of two-phase flows in three space dimensions

We present a new second-order (in space), semi-discrete, central scheme for the approximation of hyperbolic conservation laws in three space dimensions. The proposed scheme is applied to a model for two-phase, immiscible and incompressible displacement in heterogeneous porous media. Numerical simulations are presented to demonstrate its ability to approximate solutions of hyperbolic equations efficiently and accurately in petroleum reservoir simulations.