Charge-conserving grid based methods for the Vlasov–Maxwell equations

Nicolas Crouseilles; Pierre Navaro; Éric Sonnendrücker

doi:10.1016/j.crme.2014.06.012

Theoretical and numerical approaches for Vlasov–Maxwell equations

Charge-conserving grid based methods for the Vlasov–Maxwell equations

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

Comptes Rendus. Mécanique, Theoretical and numerical approaches for Vlasov-maxwell equations, Volume 342 (2014) no. 10-11, pp. 636-646.

Résumé

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 : 2014-04-11
Accepté le : 2014-06-10
Publié le : 2014-08-07

DOI : 10.1016/j.crme.2014.06.012

Keywords: Maxwell–Vlasov system, Discrete continuity equation, Finite volume method, Spectral method, Semi-Lagrangian method

Affiliations des auteurs :

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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     author = {Nicolas Crouseilles and Pierre Navaro and \'Eric Sonnendr\"ucker},
     title = {Charge-conserving grid based methods for the {Vlasov{\textendash}Maxwell} equations},
     journal = {Comptes Rendus. M\'ecanique},
     pages = {636--646},
     publisher = {Elsevier},
     volume = {342},
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     doi = {10.1016/j.crme.2014.06.012},
     language = {en},
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Nicolas Crouseilles; Pierre Navaro; Éric Sonnendrücker. Charge-conserving grid based methods for the Vlasov–Maxwell equations. Comptes Rendus. Mécanique, Theoretical and numerical approaches for Vlasov-maxwell equations, 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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Benjamin Boutin; Anaïs Crestetto; Nicolas Crouseilles; Josselin Massot Modified Lawson Methods for Vlasov Equations, SIAM Journal on Scientific Computing, Volume 46 (2024) no. 3, p. A1574 | DOI:10.1137/22m154301x
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Hongtao Liu; Xiaofeng Cai; Giovanni Lapenta; Yong Cao Conservative semi-Lagrangian kinetic scheme coupled with implicit finite element field solver for multidimensional Vlasov Maxwell system, Communications in Nonlinear Science and Numerical Simulation, Volume 102 (2021), p. 105941 | DOI:10.1016/j.cnsns.2021.105941
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Nicolas Crouseilles; Lukas Einkemmer; Erwan Faou Hamiltonian splitting for the Vlasov–Maxwell equations, Journal of Computational Physics, Volume 283 (2015), p. 224 | DOI:10.1016/j.jcp.2014.11.029
M. Pfeiffer; C.-D. Munz; S. Fasoulas Hyperbolic divergence cleaning, the electrostatic limit, and potential boundary conditions for particle-in-cell codes, Journal of Computational Physics, Volume 294 (2015), p. 547 | DOI:10.1016/j.jcp.2015.04.001

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