Diffusion with dissolution and precipitation in a porous medium : mathematical analysis and numerical approximation of a simplified model
ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Volume 41 (2007) no. 6, p. 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 : https://doi.org/10.1051/m2an:2007047
Classification:  65N12,  76S05,  80A30
Keywords: diffusion, dissolution, precipitation, kinetics, finite volume method
@article{M2AN_2007__41_6_975_0,
     author = {Bouillard, Nicolas and Eymard, Robert and Herbin, Raphaele and Montarnal, Philippe},
     title = {Diffusion with dissolution and precipitation in a porous medium : mathematical analysis and numerical approximation of a simplified model},
     journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Mod\'elisation Math\'ematique et Analyse Num\'erique},
     publisher = {EDP-Sciences},
     volume = {41},
     number = {6},
     year = {2007},
     pages = {975-1000},
     doi = {10.1051/m2an:2007047},
     zbl = {1130.76086},
     mrnumber = {2377103},
     language = {en},
     url = {http://www.numdam.org/item/M2AN_2007__41_6_975_0}
}
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: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Volume 41 (2007) no. 6, pp. 975-1000. doi : 10.1051/m2an:2007047. http://www.numdam.org/item/M2AN_2007__41_6_975_0/

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