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

Nicolas Bouillard; Robert Eymard; Raphaele Herbin; Philippe Montarnal

ESAIM: Mathematical Modelling and Numerical Analysis (2007)

- Volume: 41, Issue: 6, page 975-1000
- ISSN: 0764-583X

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topBouillard, Nicolas, et al. "Diffusion with dissolution and precipitation in a porous medium: Mathematical analysis and numerical approximation of a simplified model." ESAIM: Mathematical Modelling and Numerical Analysis 41.6 (2007): 975-1000. <http://eudml.org/doc/250079>.

@article{Bouillard2007,

abstract = {
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.
},

author = {Bouillard, Nicolas, Eymard, Robert, Herbin, Raphaele, Montarnal, Philippe},

journal = {ESAIM: Mathematical Modelling and Numerical Analysis},

keywords = {Diffusion; dissolution; precipitation; kinetics; finite volume method.; finite volume method; uniqueness; weak solution},

language = {eng},

month = {12},

number = {6},

pages = {975-1000},

publisher = {EDP Sciences},

title = {Diffusion with dissolution and precipitation in a porous medium: Mathematical analysis and numerical approximation of a simplified model},

url = {http://eudml.org/doc/250079},

volume = {41},

year = {2007},

}

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

DA - 2007/12//

PB - EDP Sciences

VL - 41

IS - 6

SP - 975

EP - 1000

AB -
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.

LA - eng

KW - Diffusion; dissolution; precipitation; kinetics; finite volume method.; finite volume method; uniqueness; weak solution

UR - http://eudml.org/doc/250079

ER -

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