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

Andres Santos; Jose M. Montanero

doi:10.1007/s10035-009-0132-8

paper

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

arXiv:0812.3022 · doi:10.1007/s10035-009-0132-8

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 ( $c \sim 1$ ) 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.

12 pages, 5 figures; v2: minor changes

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

Abstract

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