Title :

Moment preserving Fourier-Galerkin spectral methods and application to the Boltzmann equation

Author(s) :

Pareschi, Lorenzo [Auteur]
Department of Mathematics [Ferrara]
Rey, Thomas [Auteur]
Laboratoire Paul Painlevé - UMR 8524 [LPP]
Reliable numerical approximations of dissipative systems [RAPSODI]

Journal title :

SIAM Journal on Numerical Analysis

Pages :

3216-3240

Publisher :

Society for Industrial and Applied Mathematics

Publication date :

2022-12-19

ISSN :

0036-1429

English keyword(s) :

Boltzmann equation
Fourier-Galerkin spectral method
conservative methods
spectral accuracy
stability
Maxwellian equilibrium

HAL domain(s) :

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

English abstract : [en]

Spectral methods, thanks to the high accuracy and the possibility of using fast algorithms, represent an effective way to approximate collisional kinetic equations in kinetic theory. On the other hand, the loss of some ...
Show more >Spectral methods, thanks to the high accuracy and the possibility of using fast algorithms, represent an effective way to approximate collisional kinetic equations in kinetic theory. On the other hand, the loss of some local invariants can lead to the wrong long time behavior of the numerical solution. We introduce in this paper a novel Fourier-Galerkin spectral method that improves the classical spectral method by making it conservative on the moments of the approximated distribution, without sacrificing its spectral accuracy or the possibility of using fast algorithms. The method is derived directly using a constrained best approximation in the space of trigonometric polynomials and can be applied to a wide class of problems where preservation of moments is essential. We then apply the new spectral method to the evaluation of the Boltzmann collision term, and prove spectral consistency and stability of the resulting Fourier-Galerkin approximation scheme. Various numerical experiments illustrate the theoretical findings.Show less >

Language :

Anglais

Peer reviewed article :

Oui

Audience :

Internationale

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

Submission date :

2025-01-24T16:20:37Z