Convergence Analysis of a Mixed Finite Volume Scheme for an Elliptic-Parabolic System Modeling Miscible Fluid Flows in Porous Media | Zendy

Claire Chainais-Hillairet | Zendy; Jérôme Droniou | Zendy

Open Access

Convergence Analysis of a Mixed Finite Volume Scheme for an Elliptic-Parabolic System Modeling Miscible Fluid Flows in Porous Media

Author(s) -

Claire Chainais-Hillairet,

Jérôme Droniou

Publication year - 2007

Publication title -

siam journal on numerical analysis

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 2.78

H-Index - 134

eISSN - 1095-7170

pISSN - 0036-1429

DOI - 10.1137/060657236

Subject(s) - discretization , finite volume method , convergence (economics) , porous medium , mathematics , mathematical analysis , nonlinear system , dimension (graph theory) , displacement (psychology) , finite element method , mechanics , physics , porosity , materials science , thermodynamics , psychology , quantum mechanics , pure mathematics , economics , composite material , psychotherapist , economic growth

We study a finite volume discretization of a strongly coupled elliptic-parabolic PDE system describing miscible displacement in a porous medium. We discretize each equation by a finite volume scheme which allows a wide variety of unstructured grids (in any space dimension) and gives strong enough convergence for handling the nonlinear coupling of the equations. We prove the convergence of the scheme as the time and space steps go to $0$. Finally, we provide numerical results to demonstrate the efficiency of the proposed numerical scheme.

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