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.