Block preconditioners for mixed-dimensional discretization of flow in fractured porous media

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 regard 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.

Automated summary

This paper proposes an efficient numerical method for modeling single-phase flow in fractured porous media using a mixed-dimensional approach. The method introduces fractures as lower-dimensional structures and employs a mortar variable for flow coupling between matrix and fractures. Stability of the mixed finite element discretization is considered, leading to a parameter-dependent linear system with block preconditioners. The iterative method demonstrates robustness in handling discretization and physical parameters, resulting in notable reductions in iteration numbers and computational time.