Homogeneous cooling state of a low-density granular flow

The homogeneous cooling state of a granular flow of smooth spherical particles described by the Boltzmann equation is investigated by means of the direct simulation Monte Carlo method. The velocity moments and also the velocity distribution function an obtained and compared with approximate analytical results derived recently. The accuracy of a Maxwell-Boltzmann approximation with a time-dependent temperature is discussed. Besides, the simulations show that the state of uniform density is unstable to long enough wavelength perturbations so that clusters and voids spontaneously form throughout the system. The instability has the characteristic features of the clustering instability which has been observed in molecular dynamics simulations of dense fluids and predicted by hydrodynamic models of granular flows.