  This paper deals with the numerical resolution of kinetic models for systems
of self-propelled particles subject to alignment interaction and
attraction-repulsion. We focus on the kinetic model considered in [18, 17]
where alignment is taken into account in addition of an attraction-repulsion
interaction potential. We apply a discontinuous Galerkin method for the free
transport and non-local drift velocity together with a spectral method for the
velocity variable. Then, we analyse consistency and stability of the
semi-discrete scheme. We propose several numerical experiments which provide a
solid validation of the method and its underlying concepts.
