  We present in this paper detailed numerical Vlasov simulations of the
Hamiltonian Mean-Field model. This model is used as a representative of the
class of systems under long-range interactions. We check existing results on
the stability of the homogeneous situation and analyze numerical properties of
the semi-Lagrangian time-split algorithm for solving the Vlasov equation. We
also detail limitations due to finite resolution of the method.
