Geodesic
A well-balanced scheme using exact solutions to the two species Vlasov-Poisson system
Nicolas Crouseilles1 ; Mohammed Lemou2 ; Guillaume Morel3 ; Pierre Navaro4
1 Univ Rennes, Inria (Mingus team), IRMAR UMR 6625 and ENS Rennes, France
2 Univ Rennes, CNRS, IRMAR UMR 6625, France
3 IMT Atlantique, France
4 Univ Rennes, CNRS, Inria (Mingus team), IRMAR UMR 6625, France
ESAIM. Proceedings, Tome 77 (2024), pp. 267-284 Cet article a éte moissonné depuis la source EDP Sciences

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In this work, we consider the numerical approximation of the two-species Vlasov-Poisson system using Eulerian methods. A family of exact non homogeneous stationary solutions are constructed using elliptic functions. Then, specific numerical schemes are proposed to compute solutions which remain close to a given stationary solution since standard schemes fail to capture such a dynamics on coarse meshes. The strategy is based on a suitable decomposition of the solution (in the spirit of δ f approaches) which can be easily combined with any classical Vlasov solvers. For unstable dynamics, a projection technique is proposed in order to dynamically change the equilibrium. Finally, numerical tests are proposed to illustrate the good behavior of the proposed strategy.
DOI : 10.1051/proc/202477267

Nicolas Crouseilles 1 ; Mohammed Lemou 2 ; Guillaume Morel 3 ; Pierre Navaro 4

1 Univ Rennes, Inria (Mingus team), IRMAR UMR 6625 and ENS Rennes, France
2 Univ Rennes, CNRS, IRMAR UMR 6625, France
3 IMT Atlantique, France
4 Univ Rennes, CNRS, Inria (Mingus team), IRMAR UMR 6625, France 
@article{EP_2024_77_a13,
     author = {Nicolas Crouseilles and Mohammed Lemou and Guillaume Morel and Pierre Navaro},
     title = {A well-balanced scheme using exact solutions to the two species {Vlasov-Poisson} system},
     journal = {ESAIM. Proceedings},
     pages = {267--284},
     year = {2024},
     volume = {77},
     doi = {10.1051/proc/202477267},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.1051/proc/202477267/}
}
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Nicolas Crouseilles; Mohammed Lemou; Guillaume Morel; Pierre Navaro. A well-balanced scheme using exact solutions to the two species Vlasov-Poisson system. ESAIM. Proceedings, Tome 77 (2024), pp. 267-284. doi: 10.1051/proc/202477267

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