A robust implicit scheme for two-phase flow in porous media
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In this thesis we present a new implicit scheme for the numerical simulation of two-phase flow in porous media. Linear finite elements are considered for the spatial discretization. The scheme is based on the iterative IMPES approach and treats the capillary pressure term implicitly to ensure stability. Under assumption of smoothness of the capillary pressure and the phase mobility curves, we were able to prove convergence theorem for the scheme. Two dimensional numerical simulations furthermore verify the convergence. To illustrate the potential of the new scheme we compare its computational efficiency to our implementation of two other common approaches to the problem: IMPES and the fully implicit formulation solved by Newton's method. The advantage of our scheme over IMPES is improved stability for larger time-step. At the same time, it is cheaper in terms of computational costs and memory requirements compared to the Newton method.