Hydrodynamic modes, Green-Kubo relations, and velocity correlations in dilute granular gases

TL;DR

This paper derives Green-Kubo type relations for dilute granular gases, identifies hydrodynamic modes, and confirms velocity correlations through simulations, advancing understanding of granular flow dynamics.

Contribution

It introduces a generalized Green-Kubo framework for granular gases and demonstrates the presence of velocity correlations in the homogeneous cooling state.

Findings

Hydrodynamic modes can be calculated in the long wavelength limit.

Transport coefficients are expressed via generalized Green-Kubo relations.

Velocity correlations manifest in energy fluctuations and are confirmed by simulations.

Abstract

It is shown that the hydrodynamic modes of a dilute granular gas of inelastic hard spheres can be identified, and calculated in the long wavelength limit. Assuming they dominate at long times, formal expressions for the Navier-Stokes transport coefficients are derived. They can be expressed in a form that generalizes the Green-Kubo relations for molecular systems, and it is shown that they can also be evaluated by means of $N$-particle simulation methods. The form of the hydrodynamic modes to zeroth order in the gradients is used to detect the presence of inherent velocity correlations in the homogeneous cooling state, even in the low density limit. They manifest themselves in the fluctuations of the total energy of the system. The theoretical predictions are shown to be in agreement with molecular dynamics simulations. Relevant related questions deserving further attention are pointed out.