Convergence of splitting methods on rotating grids for the magnetized Vlasov equation

2024/06/14 by Nils Schild, Schild, Nils, Mario Raeth Klaus Hallatschek +3 · 1 citation
Engineering · Mathematics · #65M12 #65M25 #65Z05 #Computational Fluid Dynamics and Aerodynamics #FOS: Mathematics #FOS: Physical sciences #Fluid Dynamics and Turbulent Flows #Gas Dynamics and Kinetic Theory #Mathematical Physics (math-ph) #Numerical Analysis (math.NA)

paper · pdf · doi:10.48550/arxiv.2406.09941

openalex publication_date 2024/06/14 · openalex created_date 2024/06/18 · openalex updated_date 2026/07/28

Abstract

Semi-Lagrangian solvers for the Vlasov system offer noiseless solutions compared to Lagrangian particle methods and can handle larger time steps compared to Eulerian methods. In order to reduce the computational complexity of the interpolation steps, it is common to use a directional splitting. However, this typically yields the wrong angular velocity. In this paper, we analyze a semi-Lagrangian method that treats the v × B term with a rotational grid and combines this with a directional splitting for the remaining terms. We analyze the convergence properties of the scheme both analytically and numerically. The favorable numerical properties of the rotating grid solution are demonstrated for the case of ion Bernstein waves.

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• Solving the six-dimensional Vlasov-Maxwell System with Active Flux and Splitting Methods

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