Uniformly accurate Particle-In-Cell method for the long time two-dimensional Vlasov-Poisson equation with strong magnetic field

Nicolas Crouseilles (1, 2, 3) , Mohammed Lemou (2, 1, 4) , Florian Méhats (2, 1, 3) , Xiaofei Zhao (2, 3)

1 IPSO - Invariant Preserving SOlvers
2 IRMAR - Institut de Recherche Mathématique de Rennes
3 MINGUS - Multi-scale numerical geometric schemes
4 CNRS - Centre National de la Recherche Scientifique

In this work, we focus on the numerical resolution of the four dimensional phase space Vlasov-Poisson system subject to a strong external magnetic field. To do so, we consider a Particle-In-Cell based method, for which the characteristics are reformulated by means of the two-scale formalism, which is well-adapted to handle highly-oscillatory equations. Then, a numerical scheme is derived for the two-scale equations. The so-obtained scheme enjoys a uniform accuracy property, meaning that its accuracy does not depend on the small parameter. Several numerical results illustrate the capabilities of the method.

Mots clés: Four dimensional; Vlasov-Poisson equation; Two-scale formulation; Highly oscillatory; Kinetic models; Particle-in-Cell; Uniformly accurate

Domaines: Analyse numérique [math.NA]; Physique Numérique [physics.comp-ph]

Nicolas Crouseilles, Mohammed Lemou, Florian Méhats, Xiaofei Zhao. Uniformly accurate Particle-In-Cell method for the long time two-dimensional Vlasov-Poisson equation with strong magnetic field. Journal of Computational Physics, 2017, 346, pp.172-190. ⟨10.1016/j.jcp.2017.06.011⟩. ⟨hal-01418976⟩