  We study fluidized granular gases in a stationary state determined by the
balance between an external driving and the bulk dissipation. The two
considered situations are inspired by recent experiments, where the gravity
plays a major role as a driving mechanism: in the first case gravity acts only
in one direction and the bottom wall is vibrated, in the second case gravity
acts in both directions and no vibrating walls are present. Simulations
performed under the molecular chaos assumption show averaged profiles of
density, velocity and granular temperature which are in good agreement with the
experiments. Moreover we measure the velocity distributions which show strong
non-Gaussian behavior, as experiments pointed out, but also density
correlations accounting for clustering, at odds with the experimental results.
The hydrodynamics of the first model is discussed and an exact solution is
found for the density and granular temperature as functions of the distance
from the vibrating wall. The limitations of such a solution, in particular in a
broad layer near the wall injecting energy, are discussed.
