Hydrodynamics for granular flow at low density

TLDR

The study derives hydrodynamic equations for a dissipative hard‑sphere gas from the Boltzmann equation, highlighting the need to include linear Burnett contributions to the energy balance. The authors compute heat and momentum fluxes to Navier‑Stokes order, yielding transport coefficients expressed explicitly in terms of the restitution coefficient. The linearized equations produce dispersion relations whose stability is analyzed, and the authors demonstrate embedding these results into simpler kinetic models to enable study of more complex states.

Abstract

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.