  Analytical studies based on perturbative theory have shown that the moments
of the Probability Distribution Function (PDF) of the local smoothed velocity
divergence are expected to have a very specific dependence on the density
parameter Omega in the quasi-linear regime. This dependence is particularly
interesting as it does not involve the possible bias between the galaxy spatial
distribution and the underlying mass distribution. This implies a new and
promising method for determining a bias-independent value of Omega based on a
reliable determination of the velocity divergence PDF.
  In this paper we study the Omega dependence of the velocity divergence PDF
and its first moments in a set of N-body simulations, using the so-called
Voronoi and Delaunay methods. We show that this dependence is in agreement with
the theoretical prediction, even while the number density of velocity field
tracers has been diluted to a value comparable to that available in current
galaxy catalogues.
  In addition, we demonstrate that a sufficiently reliable determination of
these statistical quantities is also possible when the measurement of the
galaxy peculiar velocities is restricted to the one component along the
line-of-sight. Under ideal, noise-free circumstances we can successfully
discriminate between low and high Omega.
