| Issue |
ESAIM: ProcS
Volume 77, 2024
CEMRACS 2022 - Transport in physics, biology and urban traffic
|
|
|---|---|---|
| Page(s) | 267 - 284 | |
| DOI | https://doi.org/10.1051/proc/202477267 | |
| Published online | 18 November 2024 | |
A well-balanced scheme using exact solutions to the two species Vlasov-Poisson system
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
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.
© EDP Sciences, SMAI 2024
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