Velocity Distribution and Cumulants in the Unsteady Uniform Longitudinal Flow of a Granular Gas

The uniform longitudinal flow is characterized by a linear longitudinal velocity field u(x)(x, t) = a(t) x, where a(t)= a(0)/(1 + a(0)t) is the strain rate, a uniform density n(t) proportional to a(t), and a uniform granular temperature T(t). Direct simulation Monte Carlo solutions of the Boltzmann equation for inelastic hard spheres are presented for three (one positive and two negative) representative values of the initial strain rate a(0). Starting from different initial conditions, the temporal evolution of the reduced strain rate a* proportional to a(0)/root T, the non-Newtonian viscosity, the second and third velocity cumulants, and three independent marginal distribution functions has been recorded. Elimination of time in favor of the reduced strain rate a* shows that, after a few collisions per particle, different initial states are attracted to common "hydrodynamic" curves. Strong deviations from Maxwellian properties are observed from the analysis of the cumulants and the marginal distributions.