4.7 Article

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

Journal

COMPUTERS & MATHEMATICS WITH APPLICATIONS
Volume 78, Issue 9, Pages 3139-3151

Publisher

PERGAMON-ELSEVIER SCIENCE LTD
DOI: 10.1016/j.camwa.2019.04.031

Keywords

Darcy-Forchheimer; Finite volumes; Fractured porous media; Geometric multigrid

Funding

  1. European Union's Horizon 2020 research and innovation programme under the Marie Sktodowska-Curie Grant [705402]
  2. FEDER/MINECO, Spain [MTM2014-52859-P, MTM2016-75139-R]

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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. (C) 2019 Elsevier Ltd. All rights reserved.

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