Comptes Rendus
Theoretical and numerical approaches for Vlasov–Maxwell equations
Charge-conserving grid based methods for the Vlasov–Maxwell equations
Comptes Rendus. Mécanique, Volume 342 (2014) no. 10-11, pp. 636-646.

In this article, we introduce numerical schemes for the Vlasov–Maxwell equations relying on different kinds of grid-based Vlasov solvers, as opposite to PIC schemes, which enforce a discrete continuity equation. The idea underlying these schemes relies on a time-splitting scheme between configuration space and velocity space for the Vlasov equation and on the computation of the discrete current in a form that is compatible with the discrete Maxwell solver.

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DOI: 10.1016/j.crme.2014.06.012
Keywords: Maxwell–Vlasov system, Discrete continuity equation, Finite volume method, Spectral method, Semi-Lagrangian method

Nicolas Crouseilles 1; Pierre Navaro 2; Éric Sonnendrücker 3, 4

1 Inria Rennes Bretagne Atlantique, IPSO Project, France
2 IRMA – CNRS & Université de Strasbourg, France
3 Max-Planck Institute for Plasma Physics, Boltzmannstr. 2, 85748 Garching, Germany
4 Mathematics Center, TU Munich, Boltzmannstr. 3, 85747 Garching, Germany
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Nicolas Crouseilles; Pierre Navaro; Éric Sonnendrücker. Charge-conserving grid based methods for the Vlasov–Maxwell equations. Comptes Rendus. Mécanique, Volume 342 (2014) no. 10-11, pp. 636-646. doi : 10.1016/j.crme.2014.06.012. https://comptes-rendus.academie-sciences.fr/mecanique/articles/10.1016/j.crme.2014.06.012/

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