Monolithic mixed-dimensional multigrid methods for single-phase flow in fractured porous media
The method provides an efficient solver for flow in fractured porous media, a problem relevant to subsurface engineering applications such as geothermal energy and oil recovery.
This paper proposes a monolithic mixed-dimensional multigrid method for single-phase flow in fractured porous media, achieving convergence factors matching those of standard multigrid for Darcy problems. Numerical experiments demonstrate robustness with respect to fracture permeability, grid size, and number of fractures.
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 inter-grid transfer operators) in the porous matrix with their one-dimensional counterparts within the fractures, giving rise to a mixed-dimensional 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.