Title :

A convergent finite volume scheme for dissipation driven models with volume filling constraint

Author(s) :

Cancès, Clément [Auteur correspondant]
Reliable numerical approximations of dissipative systems [RAPSODI]
Zurek, Antoine [Auteur correspondant]
Institute for Analysis and Scientific Computing [Wien]

Journal title :

Numerische Mathematik

Pages :

279--328

Publisher :

Springer Verlag

Publication date :

2022

ISSN :

0029-599X

HAL domain(s) :

Mathématiques [math]/Analyse numérique [math.NA]

English abstract : [en]

In this paper we propose and study an implicit finite volume scheme for a general model which describes the evolution of the composition of a multi-component mixture in a bounded domain. We assume that the whole domain is ...
Show more >In this paper we propose and study an implicit finite volume scheme for a general model which describes the evolution of the composition of a multi-component mixture in a bounded domain. We assume that the whole domain is occupied by the different phases of the mixture which leads to a volume filling constraint. In the continuous model this constraint yields the introduction of a pressure, which should be thought as a Lagrange multiplier for the volume filling constraint. The pressure solves an elliptic equation, to be coupled with parabolic equations, possibly including cross-diffusion terms, which govern the evolution of the mixture composition. Besides the system admits an entropy structure which is at the cornerstone of our analysis. More precisely, the main objective of this work is to design a two-point flux approximation finite volume scheme which preserves the key properties of the continuous model, namely the volume filling constraint and the control of the entropy production. Thanks to these properties, and in particular the discrete entropy-entropy dissipation relation, we are able to prove the existence of solutions to the scheme and its convergence. Finally, we illustrate the behavior of our scheme through different applications.Show less >

Language :

Anglais

Popular science :

Non

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