Space-only hyperbolic approximation of the Vlasov equation

Philippe Helluy (1, 2) , Nhung Pham (1, 2) , Anaïs Crestetto (2, 1)

1 IRMA - Institut de Recherche Mathématique Avancée
2 CALVI - Scientific computation and visualization

We construct an hyperbolic approximation of the Vlasov equation in which the dependency on the velocity variable is removed. The resulting model enjoys interesting conservation and entropy properties. It can be numerically solved by standard schemes for hyperbolic systems. We present numerical results for one-dimensional classical test cases in plasma physics: Landau damping, two-stream instability

Domaines: Equations aux dérivées partielles [math.AP]

Philippe Helluy, Nhung Pham, Anaïs Crestetto. Space-only hyperbolic approximation of the Vlasov equation. ESAIM: Proceedings, 2013, 43, pp.17-36. ⟨10.1051/proc/201343002⟩. ⟨hal-00797974⟩