Block Preconditioners for Mixed-dimensional Discretization of Flow in Fractured Porous Media
For researchers in computational geosciences, this work provides efficient preconditioners for simulating flow in fractured porous media, though it is an incremental improvement over existing methods.
The paper develops block preconditioners for solving linear systems arising from mixed-dimensional discretization of flow in fractured porous media. The preconditioned iterative method shows robustness with respect to discretization and physical parameters, achieving notable reductions in iteration count and computational time.
In this paper, we are interested in an efficient numerical method for the mixed-dimensional approach to modeling single-phase flow in fractured porous media. The model introduces fractures and their intersections as lower-dimensional structures, and the mortar variable is used for flow coupling between the matrix and fractures. We consider a stable mixed finite element discretization of the problem, which results in a parameter-dependent linear system. For this, we develop block preconditioners based on the well-posedness of the discretization choice. The preconditioned iterative method demonstrates robustness with regards to discretization and physical parameters. The analytical results are verified on several examples of fracture network configurations, and notable results in reduction of number of iterations and computational time are obtained.