Finite volume approximation of degenerate two-phase flow model with unlimited air mobility

Autor: Andreianov, Boris, Eymard, Robert, Ghilani, Mustapha, Marhraoui, Nouzha
Přispěvatelé: Laboratoire de Mathématiques de Besançon (UMR 6623) (LMB), Université de Franche-Comté (UFC), Université Bourgogne Franche-Comté [COMUE] (UBFC)-Université Bourgogne Franche-Comté [COMUE] (UBFC)-Centre National de la Recherche Scientifique (CNRS)-Université de Bourgogne (UB), Laboratoire d'Analyse et de Mathématiques Appliquées (LAMA), Centre National de la Recherche Scientifique (CNRS)-Université Paris-Est Créteil Val-de-Marne - Paris 12 (UPEC UP12)-Fédération de Recherche Bézout-Université Paris-Est Marne-la-Vallée (UPEM), EMMACS, Université Moulay Ismail (UMI), PARS MI06 CNRST, CNRS-CNRST SPM08/10 No.24506, Centre National de la Recherche Scientifique (CNRS)-Université de Franche-Comté (UFC), Université Paris-Est Marne-la-Vallée (UPEM)-Fédération de Recherche Bézout-Université Paris-Est Créteil Val-de-Marne - Paris 12 (UPEC UP12)-Centre National de la Recherche Scientifique (CNRS), Université de Moulay Ismail (UMI), Université de Bourgogne (UB)-Université de Franche-Comté (UFC), Université Bourgogne Franche-Comté [COMUE] (UBFC)-Université Bourgogne Franche-Comté [COMUE] (UBFC)-Centre National de la Recherche Scientifique (CNRS)
Jazyk: angličtina
Rok vydání: 2012
Předmět:
Zdroj: Numerical Methods for Partial Differential Equations
Numerical Methods for Partial Differential Equations, Wiley, 2012, 29 (2), pp. 441-474. ⟨10.1002/num.21715⟩
ISSN: 0749-159X
1098-2426
DOI: 10.1002/num.21715⟩
Popis: International audience; Models of two-phase flows in porous media, used in petroleum engineering, lead to a coupled system of two equations, one elliptic, the other degenerate parabolic, with two unknowns: the saturation and the pressure. In view of applications in hydrogeology, we are interested at the singular limit of this model, as the ratio $\mu$ of air/liquid mobility goes to infinity, and in a comparison with the one-phase Richards model. We construct a robust finite volume scheme that can apply for large values of the parameter $\mu$. This scheme is shown to satisfy a priori estimates (the saturation is shown to remain in a fixed interval, and a discrete $\ldehun$ estimate is proved for both the pressure and a function of the saturation) which are sufficient to derive the convergence of a subsequence to a weak solution of the continuous equations, as the size of the discretization tends to zero. At the limit as the mobility of the air phase tends to infinity, we obtain the two-phase flow model introduced in the work Henry, Hilhorst and Eymard \cite{MHenry-et-al} (see also \cite{Eymard-Ghilani-Marhraoui}) which we call the quasi-Richards equation.
Databáze: OpenAIRE
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