An Asymptotically Stable Semi-Lagrangian scheme in the Quasi-neutral Limit

This paper deals with the numerical simulations of the Vlasov-Poisson equation using a phase space grid in the quasi-neutral regime. In this limit, explicit numerical schemes suffer from numerical constraints related to the small Debye length and large plasma frequency. Here, we propose a semi-Lagrangian scheme for the Vlasov-Poisson model in the quasi-neutral limit. The main ingredient relies on a reformulation of the Poisson equation derived in [4] which enables asymptotically stable simulations. This scheme has a comparable numerical cost per time step to that of an explicit Centre de Mathématiques Appliquées (UMR 7641), Ecole Polytechnique, F-91128 Palaiseau, France. [email protected] INRIA Nancy-Grand-EST (CALVI Project), and IRMA-Université de Strasbourg and CNRS, F-67084 Strasbourg cedex, France. [email protected] 1-Université de Toulouse; UPS, INSA, UT1, UTM ; Institut de Mathématiques de Toulouse; F-31062 Toulouse, France. 2-CNRS; Institut de Mathématiques de Toulouse UMR 5219; F-31062 Toulouse, France. [email protected] IRMA-Université de Strasbourg and CNRS, and INRIA NancyGrand-Est (CALVI Project), F-67084 Strasbourg cedex, France. [email protected]