Monolithic mixed-dimensional multigrid methods for single-phase flow in fractured porous media

TL;DR

This paper introduces a monolithic mixed-dimensional multigrid method for efficiently solving single-phase flow in complex fractured porous media, combining 2D and 1D multigrid components for optimal convergence.

Contribution

It presents a novel mixed-dimensional multigrid approach that effectively handles arbitrary fracture networks in porous media, improving convergence and robustness.

Findings

Convergence matches the multigrid convergence factor for Darcy problems.

Method is robust to variations in fracture permeability and grid size.

Demonstrated effectiveness across different fracture network complexities.

Abstract

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.