Hydrodynamics from Grad’s equations for weakly inelastic granular flows

We introduce and discuss Grad’s moment equations for dilute granular systems of hard spheres with dissipative collisions and variable coefficient of restitution, under the assumption of weak inelasticity. An important byproduct is that in this way we obtain an hydrodynamic description of a system of nearly elastic particles by a direct procedure from the Boltzmann equation. In particular, it is shown that the statistical correlation function plays a fundamental role in the decay of the temperature, and that the latter is described, in space homogeneous conditions, by a corrected Haff’s law.