Convergence analysis of a mixed finite volume scheme for an elliptic-parabolic system modeling miscible fluid flows in porous media

Claire Chainais-Hillairet, Jerome Droniou

Research output: Contribution to journalArticleResearchpeer-review

20 Citations (Scopus)

Abstract

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.
Original languageEnglish
Pages (from-to)2228 - 2258
Number of pages31
JournalSIAM Journal on Numerical Analysis
Volume45
Issue number5
DOIs
Publication statusPublished - 2007
Externally publishedYes

Cite this

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abstract = "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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Convergence analysis of a mixed finite volume scheme for an elliptic-parabolic system modeling miscible fluid flows in porous media. / Chainais-Hillairet, Claire; Droniou, Jerome.

In: SIAM Journal on Numerical Analysis, Vol. 45, No. 5, 2007, p. 2228 - 2258.

Research output: Contribution to journalArticleResearchpeer-review

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AU - Chainais-Hillairet, Claire

AU - Droniou, Jerome

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N2 - 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.

AB - 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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JO - SIAM Journal on Numerical Analysis

JF - SIAM Journal on Numerical Analysis

SN - 0036-1429

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