Uniformly accurate methods for three dimensional Vlasov equations under strong magnetic field with varying direction

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

1 IRMAR - Institut de Recherche Mathématique de Rennes
2 MINGUS - Multi-scale numerical geometric schemes
3 Wuhan University [China]

In this paper, we consider the three dimensional Vlasov equation with an inhomo-geneous, varying direction, strong magnetic field. Whenever the magnetic field has constant intensity, the oscillations generated by the stiff term are periodic. The homogenized model is then derived and several state-of-the-art multiscale methods, in combination with the Particle-In-Cell discretisation, are proposed for solving the Vlasov-Poisson equation. Their accuracy as much as their computational cost remain essentially independent of the strength of the magnetic field. The proposed schemes thus allow large computational steps, while the full gyro-motion can be restored by a linear interpolation in time. In the linear case, extensions are introduced for general magnetic field (varying intensity and direction). Eventually, numerical experiments are exposed to illustrate the efficiency of the methods and some long-term simulations are presented.

Mots clés: Uniformly accurate method; Varying direction; 65L20; Particle-In-Cell AMS Subject Classification: 65L05; Vlasov-Poisson equation; Three dimensions; 65L70; Strong magnetic field

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

Philippe Chartier, Nicolas Crouseilles, Mohammed Lemou, Florian Méhats, Xiaofei Zhao. Uniformly accurate methods for three dimensional Vlasov equations under strong magnetic field with varying direction. SIAM Journal on Scientific Computing, 2020, 42 (2), pp.B520-B547. ⟨10.1137/19M127402X⟩. ⟨hal-02179534⟩