Block preconditioning for mixed hybrid finite element models of two-phase flow in reservoir simulations

Although two-phase flow modeling in porous media is a typical application in the energy sector, new challenges continue to emerge in the numerical efficiency of the overall solving algorithm. Addressing the nonlinear set of governing equations in a fully implicit fashion leads to repeatedly solving a series of large-size systems of equations during a simulation, possibly at a high computational cost. The key to decreasing the iterative linear solver’s computational overhead is to provide an efficient preconditioning technique. In this work, we propose a block preconditioner specifically designed to fully exploit the 3x3 block structure of the linearized systems of equations arising from a mixed hybrid finite element discretization of Darcy’s equation. In particular, the block preconditioner takes advantage of the nearly diagonal structure of the block in position (1,1). Numerical results on realistic examples show the robustness and computational efficiency of the proposed approach.