  We perform large-scale event-driven Molecular dynamics (MD) simulations for
granular gases of particles interacting with the impact-velocity dependent
restitution coefficient. We use the simplest first-principle collision model of
viscoelastic spheres. Both cases of force-free and uniformly heated gases are
studied. We formulate a simplified model of an effective constant restitution
coefficient, which depends on a current granular temperature and compute the
effective constant restitution coefficient, using the kinetic theory. We
develop a theory of the velocity distribution function for driven gases of
viscoelastic particles and analyze evolution of granular temperature and of the
Sonine coefficients, which characterize the form of the velocity distribution
function. We observe that for not large dissipation the simulation results are
in an excellent agreement with the theory for both, homogeneous cooling state
and uniformly heated gases. At the same time a noticeable discrepancy between
the theory and MD results for the Sonine coefficients is detected for large
dissipation. We analyze the accuracy of the simplified model, based on the
effective restitution coefficient and conclude that this model can accurately
describe granular temperature. It provides also an acceptable accuracy for the
velocity distribution function for small dissipation, but fails when
dissipation is large.
