Modeling fractures as interfaces with nonmatching grids

We consider a model for fluid flow in a porous medium with a fracture. In this model, the fracture is treated as an interface between subdomains, on which specific equations have to be solved. In this article, we analyze the discrete problem, assuming that the fracture mesh and the subdomain meshes...

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Bibliographic Details
Published in:Computational geosciences 2012-09, Vol.16 (4), p.1043-1060
Main Authors: Frih, Najla, Martin, Vincent, Roberts, Jean Elizabeth, Saâda, Ali
Format: Article
Language:English
Subjects:
Computational fluid dynamics
Convergence
Earth and Environmental Science
Earth science
Earth Sciences
Finite element analysis
Finite element method
Fluid dynamics
Fluid flow
Fluids
Fracture mechanics
Geotechnical Engineering & Applied Earth Sciences
Hydrogeology
Mathematical analysis
Mathematical Modeling and Industrial Mathematics
Mathematical models
Original Paper
Porous materials
Porous media
Soil Science & Conservation
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Summary:We consider a model for fluid flow in a porous medium with a fracture. In this model, the fracture is treated as an interface between subdomains, on which specific equations have to be solved. In this article, we analyze the discrete problem, assuming that the fracture mesh and the subdomain meshes are completely independent, but that the geometry of the fracture is respected. We show that despite this nonconformity, first-order convergence is preserved with the lowest-order Raviart–Thomas(-Nedelec) mixed finite elements. Numerical simulations confirm this result.
ISSN:1420-0597
1573-1499
DOI:10.1007/s10596-012-9302-6