An explicit-extended penalty Galerkin method for solving an incompressible two-phase flow

In this paper, we present a stabilized explicit-extended penalty Galerkin method based on the implicit pressure and explicit saturation method to find the global solution for the two-phase flow in porous media at each time step. The bubble functions are employed as basis of the spatial dimensions for the extended penalty Galerkin method. The forward Euler method is applied to the temporal discretization. Since the accuracy of numerical simulations flow through porous media depends on the modeling of the injection and production well, we propose a new well model for the presented method. The details of the stability analysis for the proposed method are provided and suitable values of the penalty term and time steps are calculated. The efficiency of the method is illustrated by simulations of a waterflood in a heterogeneous oil reservoir. Comparisons are made with available literature which show the efficiency and accuracy of the proposed method.