Convergence Analysis of Asymptotic Preserving Schemes for Strongly Magnetized plasmas

Francis Filbet (1) , Luis Miguel Miguel Rodrigues (2) , Hamed Zakerzadeh (1)

1 IMT - Institut de Mathématiques de Toulouse UMR5219
2 IRMAR - Institut de Recherche Mathématique de Rennes

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.

Mots clés: Vlasov-Poisson system; High-order time discretization; Asymptotic preserving schemes; Homogeneous magnetic field; Particle methods 2010 MSC: 35Q83; 65M75; 82D10; 65L04; 65M15

Domaines: Analyse numérique [math.NA]

Francis Filbet, Luis Miguel Miguel Rodrigues, Hamed Zakerzadeh. Convergence Analysis of Asymptotic Preserving Schemes for Strongly Magnetized plasmas. Numerische Mathematik, 2021, 149 (3), pp.549-593. ⟨10.1007/s00211-021-01248-x⟩. ⟨hal-02510283v3⟩