Conservative semi-Lagrangian schemes for Vlasov equations

Nicolas Crouseilles 1, 2 Michel Mehrenberger 2, 1 Eric Sonnendrücker 2, 1
2 CALVI - Scientific computation and visualization
IRMA - Institut de Recherche Mathématique Avancée, LSIIT - Laboratoire des Sciences de l'Image, de l'Informatique et de la Télédétection, Inria Nancy - Grand Est, IECL - Institut Élie Cartan de Lorraine
Abstract : Conservative methods for the numerical solution of the Vlasov equation are developed in the context of the one-dimensional splitting. In the case of constant advection, these methods and the traditional semi-Lagrangian ones are proven to be equivalent, but the conservative methods offer the possibility to add adequate filters in order to ensure the positivity. In the non constant advection case, they present an alternative to the traditional semi-Lagrangian schemes which can suffer from bad mass conservation, in this time splitting setting.
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Journal of Computational Physics, Elsevier, 2010, pp.1927-1953. 〈10.1016/j.jcp.2009.11.007〉
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Nicolas Crouseilles, Michel Mehrenberger, Eric Sonnendrücker. Conservative semi-Lagrangian schemes for Vlasov equations. Journal of Computational Physics, Elsevier, 2010, pp.1927-1953. 〈10.1016/j.jcp.2009.11.007〉. 〈hal-00363643〉

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