A conservative and entropic method for the Vlasov–Fokker–Planck–Landau equation

Abstract

In this paper we compute numerical solutions to the Vlasov equation coupled with the Fokker–Planck–Landau collision operator using a phase space grid. On the one hand, the transport is treated by a flux conservative method and the distribution function is reconstructed to preserve energy and to control numerical oscillations. On the other hand, the collision operators are treated to preserve the conservation properties. Some results are presented in one dimension in space and three dimensions in velocity.