The hydrodynamic equations for a gas of hard spheres with dissipative dynamics are derived from the Boltzmann equation. The heat and momentum fluxes are calculated to Navier-Stokes order and the transport coefficients are determined as explicit functions of the coefficient of restitution. The dispersion relations for the corresponding linearized equations are obtained and the stability of this linear description is discussed. This requires consideration of the linear Burnett contributions to the energy balance equation from the energy sink term. Finally, it is shown how these results can be imbedded in simpler kinetic model equations with the potential for analysis of more complex states.

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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 are 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.

Using the hydrodynamic description and molecular dynamics simulations, the steady state of a fluidized granular system in the presence of gravity is studied. For an open system, the density profile exhibits a maximum, while the temperature profile goes through a minimum at high altitude, beyond that the temperature increases with the height. The existence of the minimum is explained by the hydrodynamic equations if the presence of a collisionless boundary layer is taken into account. The energy dissipated by interparticle collisions is also computed. A good agreement is found between theory and simulation. The relationship with previous works is discussed.

A study of the transport coefficients of a system of elastic hard disks based on the use of Helfand-Einstein expressions is reported. The self-diffusion, the viscosity, and the heat conductivity are examined with averaging techniques especially appropriate for event-driven molecular dynamics algorithms with periodic boundary conditions. The density and size dependence of the results are analyzed, and comparison with the predictions from Enskog's theory is carried out. In particular, the behavior of the transport coefficients in the vicinity of the fluid-solid transition is investigated and a striking power law divergence of the viscosity with density is obtained in this region, while all other examined transport coefficients show a drop in that density range in relation to the Enskog's prediction. Finally, the deviations are related to shear band instabilities and the concept of dilatancy.