A block preconditioner for two‐phase flow in porous media by mixed hybrid finite elements

In this work, we present an original block preconditioner to improve the conver-gence of Krylov solvers for the simulation of two-phase flow in porous media. Inour modeling approach, the set of coupled governing equations is addressed in afully implicit fashion, where Darcy’s law and mass conservation are discretizedin an original way by combining the mixed hybrid finite element (MHFE) andthe finite volume (FV) methods. The solution to the sequence of large-size non-symmetric linearized systems of equations that stem during a full-transient sim-ulation represents the most time and resource consuming task, thus motivatingthe need for efficient preconditioned Krylov solvers. The proposed precondi-tioner exploits the block structure of the Jacobian matrix while coping withthe nonsymmetric nature of the individual blocks. Both academic and realisticapplications have been used to challenge the preconditioner, allowing to pointout its robustness, stability and overall computational efficiency.