Diffusion with dissolution and precipitation in a porous medium : mathematical analysis and numerical approximation of a simplified model
ESAIM: Modélisation mathématique et analyse numérique, Tome 41 (2007) no. 6, pp. 975-1000.

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.

DOI : 10.1051/m2an:2007047
Classification : 65N12, 76S05, 80A30
Mots clés : diffusion, dissolution, precipitation, kinetics, finite volume method
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Bouillard, Nicolas; Eymard, Robert; Herbin, Raphaele; Montarnal, Philippe. Diffusion with dissolution and precipitation in a porous medium : mathematical analysis and numerical approximation of a simplified model. ESAIM: Modélisation mathématique et analyse numérique, Tome 41 (2007) no. 6, pp. 975-1000. doi : 10.1051/m2an:2007047. http://www.numdam.org/articles/10.1051/m2an:2007047/

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