This Demonstration simulates two colliding galaxies. Each star is initialized with a Keplerian initial velocity and circular orbit, affected only by the mass centers of the two galaxies and not by neighboring stars.
On the surface, this resembles the effects of a galaxy collision, but it is only a very rough first approximation. Much more computationally intensive simulations may take dark matter and interactions between stars into account. Even with the more complicated parameters ignored, this simulation can still provide a glimpse into how galaxies interact.