The second and third Sonine coefficients of a freely cooling granular gas revisited

Abstract

In its simplest statistical-mechanical description, a granular fluid can be modeled as composed of smooth inelastic hard spheres (with a constant coefficient of normal restitution α) whose velocity distribution function obeys the Enskog–Boltzmann equation. The basic state of a granular fluid is the homogeneous cooling state, characterized by a homogeneous, isotropic, and stationary distribution of scaled velocities, F(c). The behavior of F(c) in the domain of thermal velocities (c ~ 1) can be characterized by the two first non-trivial coefficients (a 2 and a 3) of an expansion in Sonine polynomials. The main goals of this paper are to review some of the previous efforts made to estimate (and measure in computer simulations) the α-dependence of a 2 and a 3, to report new computer simulations results of a 2 and a 3 for two-dimensional systems, and to investigate the possibility of proposing theoretical estimates of a 2 and a 3 with an optimal compromise between simplicity and accuracy.