Grad's Moment Method for a Low-Density Granular Gas. Navier-Stokes Transport Coefficients

TL;DR

This paper derives explicit Navier-Stokes transport coefficients for a granular gas using Grad's moment method, providing formulas that agree with Chapman-Enskog results and extending previous Grad-based analyses.

Contribution

It introduces explicit expressions for shear viscosity, thermal conductivity, and a new coefficient for inelastic granular gases using Grad's moment method, aligning with Chapman-Enskog results.

Findings

Derived explicit formulas for transport coefficients as functions of restitution coefficient.

Confirmed agreement with Chapman-Enskog first Sonine approximation results.

Extended Grad's moment method analysis to granular gases in different dimensions.

Abstract

The Navier-Stokes transport coefficients for a granular gas of smooth inelastic hard disks or spheres are determined from the inelastic Boltzmann equation by means of Grad's moment method. The shear viscosity $\eta$, the thermal conductivity $\kappa$ and the new transport coefficient $\mu$ (not present for elastic collisions) are explicitly obtained as nonlinear functions of the (constant) coefficient of restitution $\alpha$. The expressions of $\eta$, $\kappa$, and $\mu$ agree with those previously obtained from the Chapman-Enskog method by using the first Sonine approximation. A comparison with previous results derived from Grad's moment method for two and three dimensions is also carried out.