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

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 $η$, the thermal conductivity $κ$ and the new transport coefficient $μ$ (not present for elastic collisions) are explicitly obtained as nonlinear functions of the (constant) coefficient of restitution $α$. The expressions of $η$, $κ$, and $μ$ 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.