Geodesic
A well-balanced scheme using exact solutions to the two species Vlasov-Poisson system
Nicolas Crouseilles1 ; Mohammed Lemou2 ; Guillaume Morel3 ; Pierre Navaro4
1Univ Rennes, Inria (Mingus team), IRMAR UMR 6625 and ENS Rennes, France
2Univ Rennes, CNRS, IRMAR UMR 6625, France
3IMT Atlantique, France
4Univ 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

Voir la notice de l'article

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/}
}
TY  - JOUR
AU  - Nicolas Crouseilles
AU  - Mohammed Lemou
AU  - Guillaume Morel
AU  - Pierre Navaro
TI  - A well-balanced scheme using exact solutions to the two species Vlasov-Poisson system
JO  - ESAIM. Proceedings
PY  - 2024
SP  - 267
EP  - 284
VL  - 77
UR  - http://geodesic.mathdoc.fr/articles/10.1051/proc/202477267/
DO  - 10.1051/proc/202477267
LA  - en
ID  - EP_2024_77_a13
ER  - 
%0 Journal Article
%A Nicolas Crouseilles
%A Mohammed Lemou
%A Guillaume Morel
%A Pierre Navaro
%T A well-balanced scheme using exact solutions to the two species Vlasov-Poisson system
%J ESAIM. Proceedings
%D 2024
%P 267-284
%V 77
%U http://geodesic.mathdoc.fr/articles/10.1051/proc/202477267/
%R 10.1051/proc/202477267
%G en
%F EP_2024_77_a13
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

Cité par Sources :