A numerical method for the accurate solution of the Fokker-Planck-Landau equation in the nonhomogeneous case

A new approach for the accurate numerical solution of the Fokker-Planck-Landau (FPL) equation in the nonhomogeneous case is presented. The method couples, through a time-splitting algorithm, a finite-volume scheme for the transport with a fast spectral solver for the efficient solution of the collision operator recently introduced. The scheme allows the use of different grids in the velocity space for the transport and the collision phases. The use of a suitable explicit Runge-Kutta solver for the time integration of the collision phase permits avoid once of excessive small time steps induced by the stiffness of the diffusive collision operator. Numerical results for both space homogeneous and space nonhomogeneous situations show the efficiency and the accuracy of the present method.