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

作者：Bouillard Nicolas; Eymard Robert; Herbin Raphaele^*; Montarnal Philippe

来源：ESAIM: Mathematical Modelling and Numerical Analysis , 2007, 41(6).

DOI：10.1051/m2an:2007047

• diffusion
• dissolution
• precipitation
• kinetics
• finite volume method

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.

• 出版日期2007-12
• 单位中国地震局