Convergence of splitting methods on rotating grids for the magnetized Vlasov equation
Fuente:
arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866909864260796416 |
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| author | Schild, Nils Hallatschek, Mario Raeth Klaus Kormann, Katharina |
| author_facet | Schild, Nils Hallatschek, Mario Raeth Klaus Kormann, Katharina |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_09941 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Convergence of splitting methods on rotating grids for the magnetized Vlasov equation Schild, Nils Hallatschek, Mario Raeth Klaus Kormann, Katharina Numerical Analysis Mathematical Physics 65M12, 65M25, 65Z05 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. |
| title | Convergence of splitting methods on rotating grids for the magnetized Vlasov equation |
| topic | Numerical Analysis Mathematical Physics 65M12, 65M25, 65Z05 |
| url | https://arxiv.org/abs/2406.09941 |