On the stability of equilibrium preserving ...
Type de document :
Compte-rendu et recension critique d'ouvrage
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]
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
Fourier-Galerkin spectral method
steady-state preserving
micro-macro decomposition
local Maxwellian
stability
Discipline(s) HAL :
Mathématiques [math]
Mathématiques [math]/Analyse numérique [math.NA]
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 >
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 :
Collections :
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