On Intrinsic Formulation and Well-posedness of a Singular Limit of Two-phase Flow Equations in Porous Media - Laboratoire d'Analyse et de Mathématiques Appliquées Accéder directement au contenu
Pré-Publication, Document De Travail Année : 2011

On Intrinsic Formulation and Well-posedness of a Singular Limit of Two-phase Flow Equations in Porous Media

Mustapha Ghilani
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  • PersonId : 905142
Nouzha Marhraoui
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  • PersonId : 905143

Résumé

Starting from a two-phase flow model in porous media with the viscosity of the ''mobile'' phase going to infinity, the Generalized Richards Equation for the ''viscous'' phase: \begin{equation*} \left\{ \begin{array}{l} u_t - \div(k_w(u) \nabla p)&=& \splus - \theta \smoins \char_{[u=1]}, \\ u=1 &\hbox{or}& \grad(p + \Pc(u)) = 0 \hbox{ a.e. in } \O\times(0,T) \end{array} \right. \end{equation*} was derived in the works \cite{MHenry-et-al} and \cite{AndrEymardGhilaniMarhraoui} (see also \cite{Eymard-Ghilani-Marhraoui}). We discuss intrinsic formulations (weak solutions, renormalized solutions) of this singular limit problem, using in particular the techniques developed by Plouvier-Debaigt, Gagneux et al. \cite{PlouvierGagneux,Plouvier,ProuvierEtAl-Cras}. For the no-source case, we justify the equivalence of the Generalized Richards Equation and the classical Richards model.
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Dates et versions

hal-00606948 , version 1 (07-07-2011)
hal-00606948 , version 2 (09-08-2011)

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  • HAL Id : hal-00606948 , version 1

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Boris Andreianov, Robert Eymard, Mustapha Ghilani, Nouzha Marhraoui. On Intrinsic Formulation and Well-posedness of a Singular Limit of Two-phase Flow Equations in Porous Media. 2011. ⟨hal-00606948v1⟩
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