In this paper, we apply the CFL-less kinetic over-relaxation scheme presented in [1] to the convection equation in two space dimensions. The method is a succession of free-transport steps and collisions steps. The free transport steps are solved with Fourier discretization. The collision steps are solved with over-relaxation for achieving high order The method reaches six-order accuracy when using palindromic composition method. We apply the method to the guiding-center model in plasma physics.

We present an efficient solver for the conservative transport equation with variable coefficients in complex toroidal geometries. The solver is based on a kinetic formulation resembling the Lattice-Boltzmann approach. The chosen formalism allows obtaining an explicit and conservative scheme that requires no matrix inversion and whose CFL stability condition is independent from the poloidal dynamics. We present the method and its optimized parallel implementation on toroidal geometries. Two and three dimensional plasma physics test cases are carried out.