Titre :

On the stability of equilibrium preserving spectral methods for the homogeneous Boltzmann equation

Auteur(s) :

Pareschi, Lorenzo [Auteur]
Department of Mathematics [Ferrara]
Rey, Thomas [Auteur]
Reliable numerical approximations of dissipative systems [RAPSODI]

Titre de la revue :

Applied Mathematics Letters

Pagination :

107187

Éditeur :

Elsevier

Date de publication :

2021-11

ISSN :

0893-9659

Mot(s)-clé(s) en anglais :

Boltzmann equation
Fourier-Galerkin spectral method
steady-state preserving
micro-macro decomposition
local Maxwellian
stability

Discipline(s) HAL :

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

Résumé en anglais : [en]

Spectral methods, thanks to the high accuracy and the possibility to use fast algorithms, represent an effective way to approximate the Boltzmann collision operator. On the other hand, the loss of some local invariants ...
Lire la suite >Spectral methods, thanks to the high accuracy and the possibility to use fast algorithms, represent an effective way to approximate the Boltzmann collision operator. On the other hand, the loss of some local invariants leads to the wrong long time behavior. A way to overcome this drawback, without sacrificing spectral accuracy, has been proposed recently with the construction of equilibrium preserving spectral methods. Despite the ability to capture the steady state with arbitrary accuracy, the theoretical properties of the method have never been studied in details. In this paper, using the perturbation argument developed by Filbet and Mouhot for the homogeneous Boltzmann equation, we prove stability, convergence and spectrally accurate long time behavior of the equilibrium preserving approach.Lire moins >

Langue :

Anglais

Vulgarisation :

Non

Projet ANR :

Centre Européen pour les Mathématiques, la Physique et leurs Interactions
Modèles multi-échelles et simulation numérique hybride de semi-conducteurs

Collections :

• Laboratoire Paul Painlevé - UMR 8524

Source :

Harvested from HAL