On convergence of explicit finite volume scheme for one-dimensional three-component two-phase flow model in porous media

• Autorzy: Mostefai Mohamed Lamine , Choucha Abdelbaki , Cherif Bahri

Identyfikatory

DOI

10.1515/dema-2021-0036

• Języki publikacji: EN

Abstrakty

EN

In this work, we develop and analyze an explicit finite volume scheme for a one-dimensional nonlinear, degenerate, convection–diffusion equation having application in petroleum reservoir. The main difficulty is that the solution typically lacks regularity due to the degenerate nonlinear diffusion term. We analyze a numerical scheme corresponding to explicit discretization of the diffusion term and a Godunov scheme for the advection term. L∞ stability under appropriate CFL conditions and BV estimates are obtained. It is shown that the scheme satisfies a discrete maximum principle. Then we prove convergence of the approximate solution to the weak solution of the problem, and we mount convergence results to a weak solution of the problem in L1 . Results of numerical experiments are presented to validate the theoretical analysis.

Słowa kluczowe

EN

finite volume method; degenerate parabolic equation; nonlinear convection–diffusion; porous media

PL

metoda objętości skończonych; równanie paraboliczne; media porowate

• Wydawca: De Gruyter
• Czasopismo: Demonstratio Mathematica
• Rocznik: 2021
• Tom: Vol. 54, nr 1
• Strony: 510--526
• Opis fizyczny: Bibliogr. 21 poz., rys.

Twórcy

autor

Mostefai Mohamed Lamine

• Department of Mathematics, Laboratory of Nonlinear Partial Differential Equations, ENS Kouba, Algiers, Algeria

autor

Choucha Abdelbaki

• Department of Mathematics, Laboratory of Operator Theory and PDEs: Foundations and Applications, Faculty of Exact Sciences, University of El Oued, Algeria

autor

Cherif Bahri

• Department of Mathematics, College of Sciences and Arts, Qassim University, Ar Rass, Saudi Arabia

Bibliografia

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