Two-Scale Macro-Micro decomposition of the Vlasov equation with a strong magnetic field

Nicolas Crouseilles (1, 2) , Emmanuel Frenod (3, 4) , Sever Adrian Hirstoaga (3, 5) , Alexandre Mouton (6)

1 IPSO - Invariant Preserving SOlvers
2 IRMAR - Institut de Recherche Mathématique de Rennes
3 CALVI - Scientific computation and visualization
4 LMBA - Laboratoire de Mathématiques de Bretagne Atlantique
5 IRMA - Institut de Recherche Mathématique Avancée
6 LPP - Laboratoire Paul Painlevé - UMR 8524

In this paper, we build a Two-Scale Macro-Micro decomposition of the Vlasov equation with a strong magnetic field. This consists in writing the solution of this equation as a sum of two oscillating functions with circonscribed oscillations. The first of these functions has a shape which is close to the shape of the Two-Scale limit of the solution and the second one is a correction built to offset this imposed shape. The aim of such a decomposition is to be the starting point for the construction of Two-Scale Asymptotic-Preserving Schemes.

Mots clés: Vlasov equation; homogenization; two-scale convergence; micro-macro decomposition; asymptotic-preserving schemes

Domaines: Modélisation et simulation; Analyse fonctionnelle [math.FA]; Equations aux dérivées partielles [math.AP]; Physique des plasmas [physics.plasm-ph]

Nicolas Crouseilles, Emmanuel Frenod, Sever Adrian Hirstoaga, Alexandre Mouton. Two-Scale Macro-Micro decomposition of the Vlasov equation with a strong magnetic field. Mathematical Models and Methods in Applied Sciences, 2013, 23 (08), pp.1527--1559. ⟨10.1142/S0218202513500152⟩. ⟨hal-00638617v3⟩