Titre :

Finite volumes for a generalized Poisson-Nernst-Planck system with cross-diffusion and size exclusion

Auteur(s) :

Cancès, Clément [Auteur]
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]
Vienna University of Technology = Technische Universität Wien [TU Wien]

Titre de la manifestation scientifique :

Finite Volumes for Complex Applications X

Ville :

Strasbourg

Pays :

France

Date de début de la manifestation scientifique :

2023-10

Éditeur :

Springer

Date de publication :

2023

Mot(s)-clé(s) en anglais :

cross-diffusion
exponential fitting
free energy decay
convergence
Drift-diffusion

Discipline(s) HAL :

Mathématiques [math]/Analyse numérique [math.NA]
Mathématiques [math]/Equations aux dérivées partielles [math.AP]
Physique [physics]/Physique mathématique [math-ph]

Résumé en anglais : [en]

We present two finite volume approaches for modeling the diffusion of charged particles, specifically ions, in constrained geometries using a degenerate Poisson-Nernst-Planck system with cross-diffusion and volume filling. ...
Lire la suite >We present two finite volume approaches for modeling the diffusion of charged particles, specifically ions, in constrained geometries using a degenerate Poisson-Nernst-Planck system with cross-diffusion and volume filling. Both methods utilize a two-point flux approximation and are part of the exponentially fitted scheme framework. The only difference between the two is the selection of a Stolarsky mean for the drift term originating from a self-consistent electric potential. The first version of the scheme, referred to as (SQRA), uses a geometric mean and is an extension of the squareroot approximation scheme. The second scheme, (SG), utilizes an inverse logarithmic mean to create a generalized version of the Scharfetter-Gummel scheme. Both approaches ensure the decay of some discrete 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. Numerical simulations show that both schemes are effective for moderately small Debye lengths, with the (SG) scheme demonstrating greater robustness in the small Debye length regime.Lire moins >

Langue :

Anglais

Comité de lecture :

Oui

Audience :

Internationale

Vulgarisation :

Non

Projet ANR :

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