Weakly Frictional Granular Gases

Towards dense, realistic granular media in 2D

“…The presence of friction and the rotational degrees of freedom has been related to a random restitution coefficient [196,197], however, we disregard here this stochastic approach to a deterministic problem. Only for nearly smooth or perfectly rough particles, the system evolution and transport coefficients can be computed analytically [198][199][200]. In the intermediate range of realistic friction coefficients, 0.1 ≤ µ ≤ 1.0 rather involved implicit integral equations have to be solved numerically [193].…”

Computer-aided kinetic theory and granular gases

“…One of the goals of this paper is to show that modern computational power, in particular symbolic manipulators, can be harnessed to help obtain accurate solutions of the Boltzmann equation. To this end we present a novel method for doing so and demonstrate its power by computing the distribution function of the homogeneous cooling state, showing that (as assumed and checked in MD and other simulations, see [5] and references therein) the tail of the corresponding velocity distribution is indeed exponential. Furthermore, using the same method we obtain the linear transport coefficients for all physical values of the coefficient of normal restitution, α, (a) E-mail: henri@eng.tau.ac.il (b) E-mail: fnbarlev@post.tau.ac.il (c) E-mail: serero@eng.tau.ac.il (d) E-mail: isaac@eng.tau.ac.il for a granular gas of smooth inelastic hard spheres (previous studies obtained results which are reasonably accurate for α > 0.7 [6]).…”

“…the state of a macroscopically homogeneous and isotropic unforced granular gas, whose distribution function can be written in a scaling form in the nondimensional speed, c ≡ |c|. This state (though unstable to clustering [4,10]) has been the subject of many studies (see, e.g., [5,11] and references therein) and it also serves as a zeroth order in the Chapman-Enskog expansion employed in [6]. The HCS distribution function is a solution of eq.…”

“…The substitution of this expansion, truncated at p = 2, in the Boltzmann equation has been used to obtain values for {a p ; p = 0, 1, 2}, see [9,12]. Reference [13] presents numerical evidence that suggests that this expansion diverges and the lack of convergence is attributed to the [5,14] exponential tail of the HCS:…”

“…tail (up to an algebraic prefactor [5]). Indeed, a direct calculation of the expansion of Φ, for f (0) replaced by π (namely the contribution of the tail to the expansion), i.e.…”