Systèmes à diffusion croisée couplés via ...
Document type :
Article dans une revue scientifique: Article original
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Title :
Systèmes à diffusion croisée couplés via une interface mobile
Author(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]

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]
Journal title :
Interfaces and Free Boundaries : Mathematical Analysis, Computation and Applications
Publisher :
European Mathematical Society
Publication date :
2025
ISSN :
1463-9963
English keyword(s) :
Cross-diffusion system
Finite volume
Moving interface
Free energy dissipation
Vapor deposition
Stefan-Maxwell
Finite volume
Moving interface
Free energy dissipation
Vapor deposition
Stefan-Maxwell
HAL domain(s) :
Mathématiques [math]/Equations aux dérivées partielles [math.AP]
Mathématiques [math]/Analyse numérique [math.NA]
Mathématiques [math]/Analyse numérique [math.NA]
English abstract : [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 ...
Show more >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.Show less >
Show more >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.Show less >
Language :
Anglais
Peer reviewed article :
Oui
Audience :
Internationale
Popular science :
Non
Collections :
Source :
Submission date :
2025-01-24T12:49:53Z
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