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.
Mots-clés : 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: Mod\'elisation math\'ematique et analyse num\'erique},
pages = {975--1000},
publisher = {EDP-Sciences},
volume = {41},
number = {6},
year = {2007},
doi = {10.1051/m2an:2007047},
mrnumber = {2377103},
zbl = {1130.76086},
language = {en},
url = {http://www.numdam.org/articles/10.1051/m2an:2007047/}
}
TY - JOUR AU - Bouillard, Nicolas AU - Eymard, Robert AU - Herbin, Raphaele AU - Montarnal, Philippe TI - Diffusion with dissolution and precipitation in a porous medium : mathematical analysis and numerical approximation of a simplified model JO - ESAIM: Modélisation mathématique et analyse numérique PY - 2007 SP - 975 EP - 1000 VL - 41 IS - 6 PB - EDP-Sciences UR - http://www.numdam.org/articles/10.1051/m2an:2007047/ DO - 10.1051/m2an:2007047 LA - en ID - M2AN_2007__41_6_975_0 ER -
%0 Journal Article %A Bouillard, Nicolas %A Eymard, Robert %A Herbin, Raphaele %A Montarnal, Philippe %T Diffusion with dissolution and precipitation in a porous medium : mathematical analysis and numerical approximation of a simplified model %J ESAIM: Modélisation mathématique et analyse numérique %D 2007 %P 975-1000 %V 41 %N 6 %I EDP-Sciences %U http://www.numdam.org/articles/10.1051/m2an:2007047/ %R 10.1051/m2an:2007047 %G en %F 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: 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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