Numerical solution of two-phase flow for the advection-dominated and non-linear case

This work presents a highly efficient numerical scheme for solving immiscible, advection-dominated two-phase flow in heterogeneous porous media. The pressure equation is decoupled from the saturation equation using an IMPES approach, while the advective terms are decoupled from the capillary diffusive terms in the saturation equation through sequential operator splitting. The parabolic and hyperbolic equations are approximated in time by implicit and explicit schemes, respectively. Damped Newton linearization is applied to the implicit non-linear diffusive step. Mixed hybrid finite elements are applied to the global pressure equation and to the regularized capillary diffusion term. For both linear systems arising from the approximation procedure, an AMG preconditioned conjugate gradient solver is used. A finite volume scheme with slope limiter is applied to the advective step. Numerical comparison with standard preconditioners demonstrates the reliability of the proposed AMG-preconditioner. Benchmark examples illustrate the robustness of the method.