Vlasov simulations on an adaptive phase-space grid

Michaël Gutnic (1) , Ioana Paun (1) , Eric Sonnendrücker (1)

1 IRMA - Institut de Recherche Mathématique Avancée

The numerical resolution of the Vlasov equation is usually performedby particle methods (PIC) which consist in approximating the plasma bya finite number of particles. This method allows to obtain satisfying results with a relatively smallnumber of particles. However, it is well known that, in some cases,the numerical noise inherent to the particle method becomes tooimportant to have an accurate description of the distribution functionin phase space. To remedy to thisproblem, methods discretizing the Vlasov equation on a mesh of phasespace have been proposed. The major drawback of Vlasov methods using a uniform and fixed mesh is thattheir numerical cost is high, which makes them rather inefficient whenthe dimension of phase-space grows. For this reason we areinvestigating a method using an adaptive mesh. The adaptivemethod is overlayed to a classical semi-Lagrangian method which isbased on the conservation of the distribution function alongparticle trajectories. The phase-space grid is updated using amultiresolution technique based on interpolating wavelets.

Mots clés: Vlasov; interpolet; "Vlasov; semi-Lagrangian; adaptive; multiresolution; interpolet"

Domaines: Analyse numérique [math.NA]

Michaël Gutnic, Ioana Paun, Eric Sonnendrücker. Vlasov simulations on an adaptive phase-space grid. 2003. ⟨hal-00129681⟩