Geodesic
Diffusion with dissolution and precipitation in a porous medium : mathematical analysis and numerical approximation of a simplified model
ESAIM: Mathematical Modelling and Numerical Analysis , Tome 41 (2007) no. 6, pp. 975-1000

Voir la notice de l'article provenant de la source Numdam

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 : 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 },
     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://geodesic.mathdoc.fr/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: Mathematical Modelling and Numerical Analysis 
PY  - 2007
SP  - 975
EP  - 1000
VL  - 41
IS  - 6
PB  - EDP-Sciences
UR  - http://geodesic.mathdoc.fr/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: Mathematical Modelling and Numerical Analysis 
%D 2007
%P 975-1000
%V 41
%N 6
%I EDP-Sciences
%U http://geodesic.mathdoc.fr/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: Mathematical Modelling and Numerical Analysis , Tome 41 (2007) no. 6, pp. 975-1000. doi: 10.1051/m2an:2007047

Cité par Sources :