Geometric multigrid methods for Darcy–Forchheimer flow in fractured porous media

In this paper, we present a monolithic multigrid method for the efficient solution of flow problems in fractured porous media. Specifically, we consider a mixed-dimensional model which couples Darcy flow in the porous matrix with Forchheimer flow within the fractures. A suitable finite volume discre...

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Bibliographic Details
Published in:Computers & mathematics with applications (1987) 2019-11, Vol.78 (9), p.3139-3151
Main Authors: Arrarás, A., Gaspar, F.J., Portero, L., Rodrigo, C.
Format: Article
Language:English
Subjects:
Darcy–Forchheimer
Finite element method
Finite volumes
Fractured porous media
Fractures
Geometric multigrid
Mathematical analysis
Multigrid methods
Nonlinear equations
Operators (mathematics)
Porous media
Robustness (mathematics)
Saddle points
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Summary:In this paper, we present a monolithic multigrid method for the efficient solution of flow problems in fractured porous media. Specifically, we consider a mixed-dimensional model which couples Darcy flow in the porous matrix with Forchheimer flow within the fractures. A suitable finite volume discretization permits to reduce the coupled problem to a system of nonlinear equations with a saddle point structure. In order to solve this system, we propose a full approximation scheme (FAS) multigrid solver that appropriately deals with the mixed-dimensional nature of the problem by using mixed-dimensional smoothing and inter-grid transfer operators. Numerical experiments show that the proposed multigrid method is robust with respect to the fracture permeability, the Forchheimer coefficient and the mesh size. The case of several possibly intersecting fractures in a heterogeneous porous medium is also discussed.
ISSN:0898-1221
1873-7668
DOI:10.1016/j.camwa.2019.04.031