PARTICLE-IN-WAVELETS SCHEME FOR THE 1D VLASOV-POISSON EQUATIONS

Romain Nguyen van Yen (1) , Eric Sonnendrücker (2) , Kai Schneider (3) , Marie Farge (1)

1 LMD - Laboratoire de Météorologie Dynamique (UMR 8539)
2 IRMA - Institut de Recherche Mathématique Avancée
3 M2P2 - Modélisation et Simulation Numérique (en mécanique des fluides)

A new numerical scheme called particle-in-wavelets is proposed for the Vlasov-Poisson equations, and tested in the simplest case of one spatial dimension. The plasma distribution function is discretized using tracer particles, and the charge distribution is reconstructed using wavelet-based density estimation. The latter consists in projecting the Delta distributions corresponding to the particles onto a finite dimensional linear space spanned by a family of wavelets, which is chosen adaptively. The stability and accuracy of the scheme is supported by numerical computations of Landau damping and of the two-stream instability. By direct comparison with a reference solution obtained by a very precise semi-Lagrangian method, we show that the precision is improved roughly by a factor 3 compared to a classical P¨ scheme, for a given number of particles.

Mots clés: wavelets; particle-in-cell; Vlasov equations

Domaines: Analyse numérique [math.NA]

Romain Nguyen van Yen, Eric Sonnendrücker, Kai Schneider, Marie Farge. PARTICLE-IN-WAVELETS SCHEME FOR THE 1D VLASOV-POISSON EQUATIONS. 2010. ⟨hal-00601726⟩