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Portero Egea, Laura

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https://academica-e.unavarra.es/handle/2454/49803

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Portero Egea

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Laura

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Estadística, Informática y Matemáticas

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InaMat2. Instituto de Investigación en Materiales Avanzados y Matemáticas

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0000-0002-7521-2097

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2608

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Author: Gaspar, F. J. × Subject: Fractured porous media ×

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Now showing 1 - 2 of 2
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    PublicationOpen Access
    Geometric multigrid methods for Darcy–Forchheimer flow in fractured porous media
    (Elsevier, 2019) Arrarás Ventura, Andrés; Gaspar, F. J.; Portero Egea, Laura; Rodrigo, C.; Estadística, Informática y Matemáticas; Estatistika, Informatika eta Matematika
    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.
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    PublicationOpen Access
    Mixed-dimensional geometric multigrid methods for single-phase flow in fractured porous media
    (SIAM, 2019) Arrarás Ventura, Andrés; Gaspar, F. J.; Portero Egea, Laura; Rodrigo, C.; Estadística, Informática y Matemáticas; Estatistika, Informatika eta Matematika
    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 intergrid transfer operators) in the porous matrix with their one-dimensional counterparts within the fractures, giving rise to a mixed-dimensional geometric 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.