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Convergence analysis of an approximation to miscible fluid flows in porous media by combining mixed finite element and finite volume methods
Author(s) -
Amaziane Brahim,
El Ossmani Mustapha
Publication year - 2008
Publication title -
numerical methods for partial differential equations
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.901
H-Index - 61
eISSN - 1098-2426
pISSN - 0749-159X
DOI - 10.1002/num.20291
Subject(s) - mathematics , finite volume method , porous medium , finite element method , discretization , partial differential equation , convergence (economics) , mixed finite element method , compressibility , mathematical analysis , darcy's law , displacement (psychology) , darcy–weisbach equation , fluid dynamics , flow (mathematics) , geometry , mechanics , porosity , physics , thermodynamics , materials science , psychology , economics , composite material , psychotherapist , economic growth
This article deals with development and analysis of a numerical method for a coupled system describing miscible displacement of one incompressible fluid by another through heterogeneous porous media. A mixed finite element (MFE) method is employed to discretize the Darcy flow equation combined with a conservative finite volume (FV) method on unstructured grids for the concentration equation. It is shown that the FV scheme satisfies a discrete maximum principle. We derive L ∞ and BV estimates under an appropriate CFL condition. Then we prove convergence of the approximate solutions to a weak solution of the coupled system. Numerical results are presented to see the performance of the method in two space dimensions. © 2007 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2008