Numerical approximation of collisional plasmas by high order methods

In this paper, we investigate the approximation of the solution to the Vlasov equation coupled with the Fokker–Planck–Landau collision operator using a phase space grid. On the one hand, the algorithm is based on the conservation of the flux of particles and the distribution function is reconstructed allowing to control spurious oscillations and preserving positivity and energy. On the other hand, the method preserves the main properties of the collision operators in order to reach the correct stationary state. Several numerical results are presented in one dimension in space and three dimensions in velocity.