Fluctuating hydrodynamics for dilute granular gases

TL;DR

This paper develops a fluctuating hydrodynamics framework for dilute inelastic granular gases, revealing new fluctuating forces and differences from elastic fluids, validated by molecular dynamics simulations.

Contribution

It introduces a Boltzmann-Langevin equation for inelastic gases and derives new fluctuating hydrodynamic equations, highlighting differences from elastic fluid theories.

Findings

Fluctuating forces differ from elastic case.

Langevin equation describes transverse velocity fluctuations.

Theoretical results agree with molecular dynamics simulations.

Abstract

Starting from the kinetic equations for the fluctuations and correlations of a dilute gas of inelastic hard spheres or disks, a Boltzmann-Langevin equation for the one-particle distribution function of the homogeneous cooling state is constructed. This equation is the linear Boltzmann equation with a fluctuating white noise term. Balance equations for the fluctuating hydrodynamic fields are derived. New fluctuating forces appear as compared with the elastic limit. The particular case of the transverse velocity field is investigated in detail. Its fluctuations can be described by means of a Langevin equation, but exhibiting two main differences with the Landau-Lifshitz theory: the noise is not white, and its second moment is not determined by the shear viscosity. This shows that the fluctuation-dissipation relations for molecular fluids do not straightforwardly carry over to inelastic gases. The theoretical predictions are shown to be in good agreement with molecular dynamics simulation results.