Handling the divergence constraints in Maxwell and Vlasov-Maxwell simulationsReport as inadecuate

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1 LJLL - Laboratoire Jacques-Louis Lions 2 IRMA - Institut de Recherche Mathématique Avancée 3 IPP - Max-Planck-Institut für Plasmaphysik Garching

Abstract : The aim of this paper is to review and classify the different methods that have been developed to enable stable long time simulations of the Vlasov-Maxwell equations and the Maxwell equations with sources. These methods can be classified in two types: field correction methods and sources correction methods. The field correction methods introduce new unknowns in the equations, for which additional boundary conditions are in some cases non trivial to find. The source correction consists in computing the sources so that they satisfy a discrete continuity equation compatible with a discrete Gauss- law that needs to be defined in accordance with the discretization of the Maxwell propagation operator.

Keywords : Particle in Cell PIC method discrete continuity equation Maxwell-Vlasov system generalised Maxwell equations

Author: Martin Campos Pinto - Marie Mounier - Eric Sonnendrücker -

Source: https://hal.archives-ouvertes.fr/


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