Comptes Rendus
no. 10-11
Theoretical and numerical approaches for Vlasov–Maxwell equations
Charge-conserving grid based methods for the Vlasov–Maxwell equations
Nicolas Crouseilles1  ; Pierre Navaro2  ; Éric Sonnendrücker3, 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
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.

Reçu le :
Accepté le :
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DOI : 10.1016/j.crme.2014.06.012
Mots clés : 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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     title = {Charge-conserving grid based methods for the {Vlasov{\textendash}Maxwell} equations},
     journal = {Comptes Rendus. M\'ecanique},
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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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[5] Esirkepov; T. Zh Exact charge conservation scheme for particle-in-cell simulation with an arbitrary form-factor, Comput. Phys. Commun., Volume 135 (2001), pp. 144-153

[6] T. Umeda; Y. Omura; T. Tominaga; H. Matsumoto A new charge conservation method in electromagnetic particle-in-cell simulations, Comput. Phys. Commun., Volume 156 (2004), pp. 73-85

[7] N.J. Sircombe; T.D. Arber VALIS: a split-conservative scheme for the relativistic 2D Vlasov–Maxwell system, J. Comput. Phys., Volume 228 (2009), pp. 4773-4788

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