Title :

Convergence and long-time behavior of finite volumes for a generalized Poisson-Nernst-Planck system with cross-diffusion and size exclusion

Author(s) :

Cancès, Clément [Auteur]
Laboratoire Paul Painlevé - UMR 8524 [LPP]
Reliable numerical approximations of dissipative systems [RAPSODI]
Herda, Maxime [Auteur]
Reliable numerical approximations of dissipative systems [RAPSODI]
Laboratoire Paul Painlevé - UMR 8524 [LPP]
Massimini, Annamaria [Auteur]
MATHematics for MatERIALS [MATHERIALS]
Centre d'Enseignement et de Recherche en Mathématiques et Calcul Scientifique [CERMICS]

English keyword(s) :

Drift-diffusion
Cross-diffusion
Exponential fitting
Free energy decay

HAL domain(s) :

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

English abstract : [en]

We present a finite volume scheme for modeling the diffusion of charged particles, specifically ions, in constrained geometries using a degenerate Poisson-Nernst-Planck system with size exclusion yielding cross-diffusion. ...
Show more >We present a finite volume scheme for modeling the diffusion of charged particles, specifically ions, in constrained geometries using a degenerate Poisson-Nernst-Planck system with size exclusion yielding cross-diffusion. Our method utilizes a two-point flux approximation and is part of the exponentially fitted scheme framework. The scheme is shown to be thermodynamically consistent, as it ensures the decay of some discrete version of the free energy. Classical numerical analysis results -existence of discrete solution, convergence of the scheme as the grid size and the time step go to 0 -follow. We also investigate the long-time behavior of the scheme, both from a theoretical and numerical point of view. Numerical simulations confirm our findings, but also point out some possibly very slow convergence towards equilibrium of the system under consideration.Show less >

Language :

Anglais

ANR Project :

Centre Européen pour les Mathématiques, la Physique et leurs Interactions
Systèmes de diffusion croisée sur des domaines en mouvement

Collections :

• Laboratoire Paul Painlevé - UMR 8524

Source :

Harvested from HAL