Grad's moment method for a granular fluid at moderate densities. Navier-Stokes transport coefficients

TL;DR

This paper explicitly derives the Navier-Stokes transport coefficients for a dense granular fluid using Grad's moment method, demonstrating agreement with Chapman-Enskog results and extending applicability to moderate densities and dissipation levels.

Contribution

It provides explicit formulas for transport coefficients of granular fluids at moderate densities using Grad's moment method, confirming their equivalence with Chapman-Enskog results.

Findings

Transport coefficients depend on restitution and volume fraction.

Results agree with Chapman-Enskog method.

Applicable to moderate densities and dissipation levels.

Abstract

The Navier-Stokes transport coefficients of a granular dense fluid of smooth inelastic hard disks or spheres are explicitly determined by solving the inelastic Enskog equation by means of Grad's moment method. The transport coefficients are explicitly determined as functions of the (constant) coefficient of restitution and the solid volume fraction. In addition, the cooling rate is also calculated to first order in the spatial gradients. The calculations are performed for an arbitrary number of dimensions. The results are not limited to small dissipation and are expected to apply at moderate densities. It is found that the expressions of the Navier-Stokes transport coefficients and the cooling rate agree with those previously obtained from the Chapman-Enskog method by using the leading terms in a Sonine polynomial expansion. This shows the equivalence between both methods for granular fluids in the Navier-Stokes approximation. A comparison with previous results derived from Grad's moment method for inelastic disks and spheres is also carried out.