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Diffusion with dissolution and precipitation in a porous medium: Mathematical analysis and numerical approximation of a simplified model

Published online by Cambridge University Press:  15 December 2007

Nicolas Bouillard ,
Robert Eymard ,
Raphaele Herbin  and
Philippe Montarnal
Nicolas Bouillard
Affiliation:
CEA/Saclay, DM2S/SFME/MTMS, Bât. 454 p. 18, 91191 Gif-sur-Yvette Cedex, France.
Robert Eymard
Affiliation:
Université de Marne-la-Vallée, 5 boulevard Descartes, 77454 Champs-sur-Marne, France.
Raphaele Herbin
Affiliation:
Université de Provence, LATP, UMR 6632, 39 rue Joliot Curie, 13453 Marseille, France. Raphaele.Herbin@cmi.univ-mrs.fr
Philippe Montarnal
Affiliation:
CEA/Saclay, DM2S/SFME/MTMS, Bât. 454 p. 17, 91191 Gif-sur-Yvette Cedex, France.
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Abstract

Modeling the kinetics of a precipitation dissolution reaction occurring in a porous medium where diffusion also takes place leads to a system of two parabolic equations and one ordinary differential equation coupled with a stiff reaction term. This system is discretized by a finite volume scheme which is suitable for the approximation of the discontinuous reaction term of unknown sign. Discrete solutions are shown to exist and converge towards a weak solution of the continuous problem. Uniqueness is proved under a Lipschitz condition on the equilibrium gap function. Numerical tests are shown which prove the efficiency of the scheme.

Keywords

Diffusiondissolutionprecipitationkineticsfinite volume method.
Type
Research Article
Information
ESAIM: Mathematical Modelling and Numerical Analysis , Volume 41 , Issue 6 , November 2007 , pp. 975 - 1000
Copyright
© EDP Sciences, SMAI, 2007

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