A strategy to make efficient simulations of systems of several thousan
d particles interacting via a piecewise constant potential is describe
d. A performance of several million collisions per hour is perfectly a
ttainable in present day standard workstations. This program is partic
ularly appropriate for hydrodynamic studies at a microscopic level in
situations near or far from thermodynamic equilibrium. Two illustrativ
e applications are summarily described: free thermal convection and Po
iseuille flux.