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 $\alpha$) 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, $F(\mathbf{c})$. The behavior of $F(\mathbf{c})$ 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 $\alpha$-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.

arXiv comment12 pages, 5 figures; v2: minor changes

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• Homogeneous states in driven granular mixtures: Enskog kinetic theory versus molecular dynamics simulations
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• Kinetic Theory and Memory Effects of Homogeneous Inelastic Granular Gases under Nonlinear Drag
• Relative entropy of freely cooling granular gases. A molecular dynamics study
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• Translational and rotational non-Gaussianities in homogeneous freely evolving granular gases
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