Expansion of a singularly perturbed equation with a two-scale converging convection term

Mouton, Alexandre

Document type :

Compte-rendu et recension critique d'ouvrage

DOI :

10.3934/dcdss.2016058

Title :

Expansion of a singularly perturbed equation with a two-scale converging convection term

Author(s) :

Mouton, Alexandre [Auteur]

Laboratoire Paul Painlevé - UMR 8524 [LPP]

Journal title :

Discrete and Continuous Dynamical Systems - Series S

Pages :

1447-1473

Publisher :

American Institute of Mathematical Sciences

Publication date :

2016

ISSN :

1937-1632

English keyword(s) :

Vlasov equation
convection equation
Gyrokinetic approximations
Two-scale convergence

HAL domain(s) :

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

English abstract : [en]

In many physical contexts, evolution convection equations may present some very large amplitude convective terms. As an example, in the context of magnetic confinement fusion, the distribution function that describes the ...
Show more >In many physical contexts, evolution convection equations may present some very large amplitude convective terms. As an example, in the context of magnetic confinement fusion, the distribution function that describes the plasma satisfies the Vlasov equation in which some terms are of the same order as $\epsilon^{-1}$, $\epsilon \ll 1$ being the characteristic gyrokinetic period of the particles around the magnetic lines. In this paper, we aim to present a model hierarchy for modeling the distribution function for any value of $\epsilon$ by using some two-scale convergence tools. Following Fr\'enod \& Sonnendr\"ucker's recent work, we choose the framework of a singularly perturbed convection equation where the convective terms admit either a high amplitude part or a an oscillating part with high frequency $\epsilon^{-1} \gg 1$. In this abstract framework, we derive an expansion with respect to the small parameter $\epsilon$ and we recursively identify each term of this expansion. Finally, we apply this new model hierarchy to the context of a linear Vlasov equation in three physical contexts linked to the magnetic confinement fusion and the evolution of charged particle beams.Show less >

Language :

Anglais

Popular science :

Non

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