Grad’s equations and hydrodynamics for weakly inelastic granular flows

Abstract

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 by-product is that in this way we obtain the hydrodynamic description of a system of nearly elastic particles by a direct procedure from the Boltzmann equation, without resorting to any homogeneous cooling state assumption. Several crucial results of the pertinent literature are recovered in the present physical context in which deviation from elastic scattering is of the same order as the Knudsen number. In particular, the correlation function plays a fundamental role in the decay of the temperature, and the latter is described asymptotically, in space homogeneous conditions, by a corrected Haff’s law.