  In this work, we discuss kinetic descriptions of flocking models, of the
so-called Cucker-Smale and Motsch-Tadmor types. These models are given by
Vlasov-type equations where the interactions taken into account are only given
long-range bi-particles interaction potential. We introduce a new exact
rescaling velocity method, inspired by a recent work of Filbet and Rey,
allowing to observe numerically the flocking behavior of the solutions to these
equations, without a need of remeshing or taking a very fine grid in the
velocity space. To stabilize the exact method, we also introduce a modification
of the classical upwind finite volume scheme which preserves the physical
properties of the solution, such as momentum conservation.
