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Gradient Discretization of Hybrid Dimensional Darcy Flows in Fractured Porous Media

By Konstantin Brenner, Mayya Groza, Cindy Guichard, Gilles Lebeau and Roland Masson

Abstract

International audienceThis article deals with the discretization of hybrid dimensional model of Darcy flow in fractured porous media. These models couple the flow in the fractures represented as the surfaces of codimension one with the flow in the surrounding matrix. The convergence analysis is carried out in the framework of Gradient schemes which accounts for a large family of conforming and nonconforming dis-cretizations. The Vertex Approximate Gradient (VAG) scheme and the Hybrid Finite Volume (HFV) scheme are applied to such models and are shown to verify the Gradient scheme framework. Our theoretical results are confirmed by a few numerical experiments performed both on tetrahedral and hexahedral meshes in heterogeneous isotropic and anisotropic media

Topics: [MATH] Mathematics [math]
Publisher: HAL CCSD
Year: 2014
OAI identifier: oai:HAL:hal-01313351v1
Provided by: Hal-Diderot

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