Modeling of two-phase filtration using "velocity-saturation" variables

In this paper, we propose a numerical method for solving the problem of a two-phase immiscible flow in porous media in terms of velocity-saturation variables. The velocity equations are solved by a standard control-volume method on a rectangular grid. The saturation equation is solved using an explicit weighted essentially non-oscillatory (WENO) scheme with the Runge-Kutta time discretization. It is shown that the solution is in good agreement with the experimental results obtained by R.A Dawe and C.A. Grattoni.