We study fluidized granular gases in a stationary state determined by the b
alance between external driving and bulk dissipation. The two considered si
tuations are inspired by recent experiments, where gravity plays a major ro
le as a driving mechanism: in the first case, gravity acts only in one dire
ction and the bottom wall is vibrated: in the second case, gravity acts in
both directions and no vibrating walls are present. Simulations performed u
nder the molecular chaos assumption show averaged profiles of density, velo
city, and granular temperature that are in good agreement with the experime
nts. Moreover. we measure velocity distributions that show strong non-Gauss
ian behavior, as experiments pointed out, but also density correlations acc
ounting for clustering, at odds with the experimental results. The hydrodyn
amics of the first model is discussed and an exact solution is found for th
e density and granular temperature as functions of the distance from the vi
brating wall. The limitations of such a solution, in particular in a broad
layer near the wall injecting energy, are discussed.