Diffusion with dissolution and precipitation in a porous medium: Mathematical analysis and numerical approximation of a simplified model
Bât. 454 p. 18, 91191 Gif-sur-Yvette Cedex, France.
2 Université de Marne-la-Vallée, 5 boulevard Descartes, 77454 Champs-sur-Marne, France.
3 Université de Provence, LATP, UMR 6632, 39 rue Joliot Curie, 13453 Marseille, France. Raphaele.Herbin@cmi.univ-mrs.fr
4 CEA/Saclay, DM2S/SFME/MTMS, Bât. 454 p. 17, 91191 Gif-sur-Yvette Cedex, France.
Revised: 10 November 2006
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.
Mathematics Subject Classification: 65N12 / 76S05 / 80A30
Key words: Diffusion / dissolution / precipitation / kinetics / finite volume method.
© EDP Sciences, SMAI, 2007