Titre :

Systèmes à diffusion croisée couplés via une interface mobile

Auteur(s) :

Cancès, Clément [Auteur]
Laboratoire Paul Painlevé - UMR 8524 [LPP]
Reliable numerical approximations of dissipative systems [RAPSODI]
Cauvin-Vila, Jean [Auteur]
Vienna University of Technology = Technische Universität Wien [TU Wien]
Chainais-Hillairet, Claire [Auteur]
Reliable numerical approximations of dissipative systems [RAPSODI]
Laboratoire Paul Painlevé - UMR 8524 [LPP]
Ehrlacher, Virginie [Auteur]
École nationale des ponts et chaussées [ENPC]
Centre d'Enseignement et de Recherche en Mathématiques et Calcul Scientifique [CERMICS]
MATHematics for MatERIALS [MATHERIALS]

Titre de la revue :

Interfaces and Free Boundaries : Mathematical Analysis, Computation and Applications

Éditeur :

European Mathematical Society

Date de publication :

2025

ISSN :

1463-9963

Mot(s)-clé(s) en anglais :

Cross-diffusion system
Finite volume
Moving interface
Free energy dissipation
Vapor deposition
Stefan-Maxwell

Discipline(s) HAL :

Mathématiques [math]/Equations aux dérivées partielles [math.AP]
Mathématiques [math]/Analyse numérique [math.NA]

Résumé en anglais : [en]

We propose and study a one-dimensional model which consists of two cross-diffusion systems coupled via a moving interface. The motivation stems from the modelling of complex diffusion processes in the context of the vapor ...
Lire la suite >We propose and study a one-dimensional model which consists of two cross-diffusion systems coupled via a moving interface. The motivation stems from the modelling of complex diffusion processes in the context of the vapor deposition of thin films. In our model, cross-diffusion of the various chemical species can be respectively modelled by a size-exclusion system for the solid phase and the Stefan-Maxwell system for the gaseous phase. The coupling between the two phases is modelled by linear phase transition laws of Butler-Volmer type, resulting in an interface evolution. The continuous properties of the model are investigated, in particular its entropy variational structure and stationary states. We introduce a two-point flux approximation finite volume scheme. The moving interface is addressed with a moving-mesh approach, where the mesh is locally deformed around the interface. The resulting discrete nonlinear system is shown to admit a solution that preserves the main properties of the continuous system, namely: mass conservation, nonnegativity, volume-filling constraints, decay of the free energy and asymptotics. In particular, the moving-mesh approach is compatible with the entropy structure of the continuous model. Numerical results illustrate these properties and the dynamics of the model.Lire moins >

Langue :

Anglais

Comité de lecture :

Oui

Audience :

Internationale

Vulgarisation :

Non

Projet ANR :

Systèmes de diffusion croisée sur des domaines en mouvement

Collections :

• Laboratoire Paul Painlevé - UMR 8524

Source :

Harvested from HAL