Semi-Godunov schemes for multiphase flows in porous media

We describe a class of finite volume schemes for 2 × 2 systems of conservations laws based on a “local” decomposition of the system into a series of single conservation laws but with discontinuous coefficients. The resulting schemes are based on Godunov type solvers of the reduced equations. These schemes are very easy to implement since they do not use detailed information about the eigenstructure of the full system. We illustrate the efficiency of the schemes on a variety of numerical experiments focusing on three-phase flows in porous media and show that they are robust and approximate the flow very well, even in the presence of gravity.