Title :

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

Author(s) :

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

Journal title :

Applied Mathematics Letters

Pages :

107187

Publisher :

Elsevier

Publication date :

2021-11

ISSN :

0893-9659

English keyword(s) :

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

HAL domain(s) :

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

English abstract : [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 ...
Show more >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.Show less >

Language :

Anglais

Popular science :

Non

ANR Project :

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