Adaptive time-splitting scheme for two-phase flow in heterogeneous porous media

In the present paper, an adaptive time-splitting scheme is introduced to investigate the problem of two-phase flow in heterogeneous porous media. The pressure and saturation equations are coupled by the capillary pressure which is linearized in terms of saturation. An IMplicit Pressure Explicit Saturation (IMPES) scheme is used to solve the problem under consideration. We use the time schemes for the pressure and saturation equations. The external time interval is divided into two levels, the first level is for the pressure, the second one is for the saturation. This method can reduce the computational cost arisen from the implicit solution of the pressure equation and the rapid changes in saturation. The time-step size for saturation equation is adaptive under computing and satisfying the Courant–Friedrichs–Lewy (CFL