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

Abstract

In this work, we present an original block preconditioner to improve the convergence of Krylov solvers for the simulation of two-phase flow in porous media. In our modeling approach, the set of coupled governing equations is addressed in a fully implicit fashion, where Darcy's law and mass conservation are discretized in an original way by combining the mixed hybrid finite element (MHFE) and the finite volume (FV) methods. The solution to the sequence of large-size nonsymmetric linearized systems of equations that stem during a full-transient simulation represents the most time and resource consuming task, thus motivating the need for efficient preconditioned Krylov solvers. The proposed preconditioner exploits the block structure of the Jacobian matrix while coping with the nonsymmetric nature of the individual blocks. Both academic and realistic applications have been used to challenge the preconditioner, allowing to point out its robustness, stability and overall computational efficiency.

Modified Picard with multigrid method for two‐phase flow problems in rigid porous media

“…Recently, different methods based on a Schur Complement Reduction have been presented 36,37 . In Reference 38, the authors consider an original block preconditioner which exploits the block structure of the Jacobian matrix while coping with the nonsymmetric nature of the individual blocks. Same authors propose in Reference 39 a novel preconditioning technique (EDFA) based on the approximation of the decoupling factors of the system matrix by using appropriate restriction operators for the sake of the Schur complement computation.…”