2020/03/18 by Francis Filbet, Filbet, Francis, L. Miguel Rodrigues +3 · 3 citations
Engineering · Mathematics · Physics and Astronomy · #Advanced Numerical Methods in Computational Mathematics #Computational Fluid Dynamics and Aerodynamics #FOS: Mathematics #Gas Dynamics and Kinetic Theory #Magnetic confinement fusion research #Numerical Analysis (math.NA)
paper · pdf · doi:10.48550/arxiv.2003.08104
openalex publication_date 2020/03/18 · openalex created_date 2022/07/26 · openalex updated_date 2026/07/28
The present paper is devoted to the convergence analysis of a class of asymptotic preserving particle schemes [Filbet & Rodrigues, SIAM J. Numer. Anal., 54 (2) (2016)] for the Vlasov equation with a strong external magnetic field. In this regime, classical Particle-In-Cell (PIC) methods are subject to quite restrictive stability constraints on the time and space steps, due to the small Larmor radius and plasma frequency. The asymptotic preserving discretization that we are going to study removes such a constraint while capturing the large-scale dynamics, even when the discretization (in time and space) is too coarse to capture fastest scales. Our error bounds are explicit regarding the discretization, stiffness parameter, initial data and time.