2018/11/06 by A. Arrarás, Arrarás, Andrés, Francisco J. Gaspar +5 · 1 citation
Engineering · #65F10 #65N22 #65N55 #76S05 #Advanced Numerical Analysis Techniques #Advanced Numerical Methods in Computational Mathematics #FOS: Mathematics #Numerical Analysis (math.NA) #Numerical methods in engineering
paper · pdf · doi:10.48550/arxiv.1811.02988
openalex publication_date 2018/11/06 · openalex created_date 2022/08/02 · openalex updated_date 2026/07/28
In this paper, we present a monolithic multigrid method for the efficient\nsolution of flow problems in fractured porous media. Specifically, we consider\na mixed-dimensional model which couples Darcy flow in the porous matrix with\nForchheimer flow within the fractures. A suitable finite volume discretization\npermits to reduce the coupled problem to a system of nonlinear equations with a\nsaddle point structure. In order to solve this system, we propose a full\napproximation scheme (FAS) multigrid solver that appropriately deals with the\nmixed-dimensional nature of the problem by using mixed-dimensional smoothing\nand inter-grid transfer operators. Remarkably, the nonlinearity is localized in\nthe fractures, and no coupling between the porous matrix and the fracture\nunknowns is needed in the smoothing procedure. Numerical experiments show that\nthe proposed multigrid method is robust with respect to the fracture\npermeability, the Forchheimer coefficient and the mesh size.\n