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

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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.

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Authors and Affiliations

  1. Departamento de Física, Universidad de Extremadura, 06071, Badajoz, Spain

    Andrés Santos

  2. Departamento de Ingeniería Mecánica, Energética y de los Materiales, Universidad de Extremadura, 06071, Badajoz, Spain

    José María Montanero

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  1. Andrés Santos
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  2. José María Montanero
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Correspondence to Andrés Santos.

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Santos, A., Montanero, J.M. The second and third Sonine coefficients of a freely cooling granular gas revisited. Granular Matter 11, 157–168 (2009). https://doi.org/10.1007/s10035-009-0132-8

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  • DOI: https://doi.org/10.1007/s10035-009-0132-8

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