2019/07/10 by Philippe Chartier, Chartier, Philippe, Nicolas Crouseilles +7 · 2 citations
Computer Science · Engineering · Mathematics · #65L05 #65L20 #65L70 #Advanced Mathematical Modeling in Engineering #Advanced Numerical Methods in Computational Mathematics #Computational Physics (physics.comp-ph) #FOS: Mathematics #FOS: Physical sciences #Gas Dynamics and Kinetic Theory #Numerical Analysis (math.NA)
paper · pdf · doi:10.48550/arxiv.1907.04851
openalex publication_date 2019/07/10 · openalex created_date 2019/07/23 · openalex updated_date 2026/07/28
In this paper, we consider the three dimensional Vlasov equation with an inhomogeneous, 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.