Handling the divergence constraints in Maxwell and Vlasov-Maxwell simulations

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• 作者：Martin Campos Pinto^a ; ^b ; Marie Mounier^c ; Eric Sonnendrü ; cker ; ^d ; ^e ; ^{sonnen@ipp.mpg.de" class="auth_mail" title="E-mail the corresponding author}
• 关键词：Maxwell&ndash ; Vlasov system ; Generalised Maxwell equations ; Discrete continuity equation ; Particle in Cell (PIC) method
• 刊名：Applied Mathematics and Computation
• 出版年：2016
• 出版时间：1 January 2016
• 年：2016
• 卷：272
• 期：part_P2
• 页码：403-419
• 全文大小：2396 K

文摘

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 given sources. These methods can be classified in two types: field correction methods and source 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.