DIFFUSION WITH DISSOLUTION AND PRECIPITATION IN A POROUS MEDIUM: MATHEMATICAL ANALYSIS AND NUMERICAL APPROXIMATION OF A SIMPLIFIED MODEL ∗

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