Conservative numerical schemes for the radial Vlasov-Poisson system: stability and Landau Damping
Résumé
In this paper, we build numerical conservative schemes for the radial Vlasov-Poisson system in order to observe the behavior of solutions around steady states. These schemes are based on finite differences method and provide the conservation of the mass ($L^1$ norm) and the Hamiltonian. To assure these properties and the convergence of the schemes we treat in particular the problem of singularities linked to the radial geometry. For the moment, this first version of this paper give the expression of the schemes and proves the conservational properties The next version, coming very soon, will add the visualization of the stable behavior and of the Landau Damping phenomenon.
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