Diffusion with dissolution and precipitation in a porous medium: Mathematical analysis and numerical approximation of a simplified model
| Autor: | Raphaèle Herbin, Robert Eymard, Philippe Montarnal, Nicolas Bouillard |
|---|---|
| Rok vydání: | 2007 |
| Předmět: |
Numerical Analysis
Finite volume method Discretization Differential equation Applied Mathematics Weak solution Mathematical analysis 010103 numerical & computational mathematics Lipschitz continuity 01 natural sciences Parabolic partial differential equation 010101 applied mathematics Computational Mathematics Modeling and Simulation Ordinary differential equation Reaction–diffusion system 0101 mathematics Analysis Mathematics |
| Zdroj: | ESAIM: Mathematical Modelling and Numerical Analysis. 41:975-1000 |
| ISSN: | 1290-3841 0764-583X |
| DOI: | 10.1051/m2an:2007047 |
| Popis: | 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. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
|