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

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.