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