In this work, we present a new implicit scheme for two-phase flow in porous media. The proposed scheme is based on the iterative IMPES (IMplicit Pressure Explicit Saturation) method and, therefore, preserves its efficiency in treatment of nonlinearities, while relaxing the time step condition common for explicit methods. At the same time, it does not involve costly computation of Jacobian matrix required for generic Newtons type methods. Implicit treatment of capillary pressure term ensures the stability and convergence properties of the new scheme. This choice of stabilization is supported by mathematical analysis of the method which also includes the rigorous proof of convergence. Our numerical results indicate that the scheme has superior performance compared with standard IMPES and fully implicit methods on benchmark problems.
展开▼
