This paper deals with the efficient numerical solution of single-phase flow problems in fractured porous media. A monolithic multigrid method is proposed for solving two-dimensional arbitrary fracture networks with vertical and/or horizontal possibly intersecting fractures. The key point is to combine two-dimensional multigrid components (smoother and intergrid transfer operators) in the porous matrix with their one-dimensional counterparts within the fractures, giving rise to a mixed-dimensional geometric multigrid method. This combination seems to be optimal since it provides an algorithm whose convergence matches the multigrid convergence factor for solving the Darcy problem. Several numerical experiments are presented to demonstrate the robustness of the monolithic mixed-dimensional multigrid method with respect to the permeability of the fractures, the grid size, and the number of fractures in the network.

Additional Metadata
Keywords Fracture network, Fractured porous media, Monolithic multigrid method, Single-phase flow, Vanka smoother
Persistent URL dx.doi.org/10.1137/18M1224751
Journal SIAM Journal on Scientific Computing
Citation
Arraras, A, Gaspar, F.J, Portero, L, & Rodrigo, C. (2019). Mixed-dimensional geometric multigrid methods for single-phase flow in fractured porous media. SIAM Journal on Scientific Computing, 41(5), B1082–B1114. doi:10.1137/18M1224751