Convergence of Splitting Methods on Rotating Grids for the Magnetized Vlasov Equation
Nils Schild, Mario Räth, Klaus Hallatschek, Katharina Kormann
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 $v \times B$ 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.
BibTeX
@article{Schild_2025,
title={Convergence of Splitting Methods on Rotating Grids for the Magnetized Vlasov Equation},
volume={47},
ISSN={1095-7197},
url={http://dx.doi.org/10.1137/24m1659327},
DOI={10.1137/24m1659327},
number={5},
journal={SIAM Journal on Scientific Computing},
publisher={Society for Industrial & Applied Mathematics (SIAM)},
author={Schild, Nils and Räth, Mario and Hallatschek, Klaus and Kormann, Katharina},
year={2025},
month=oct,
pages={B1272–B1292} }