Conservative numerical schemes for the radial Vlasov-Poisson system: stability and Landau Damping

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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Source https://hal.science/hal-00958414
Author Rigault, Cyril
Maintainer CCSD
Last Updated May 6, 2026, 01:45 (UTC)
Created May 6, 2026, 01:45 (UTC)
Identifier hal-00958414
Language en
Rights https://about.hal.science/hal-authorisation-v1/
contributor Laboratoire Jacques-Louis Lions (LJLL) ; Université Pierre et Marie Curie - Paris 6 (UPMC)-Université Paris Diderot - Paris 7 (UPD7)-Centre National de la Recherche Scientifique (CNRS)
creator Rigault, Cyril
date 2014-03-11T00:00:00
harvest_object_id 5bbd759a-6256-42dc-a98b-2fd71454fe3b
harvest_source_id 3374d638-d20b-4672-ba96-a23232d55657
harvest_source_title test moissonnage SELUNE
metadata_modified 2024-05-02T00:00:00
set_spec type:UNDEFINED