Constitutive Relations for Rapid Granular Flow of Smooth Spheres: Generalized Rational Approximation to the Sum of the Chapman–Enskog Expansion

N. Sela and I. Goldhirsch (1998, J. Fluid Mech.361, 41–74) have used the Chapman–Enskog expansion to derive constitutive relations for the pressure deviator P, heat flux q, and rate of energy loss Γ for rapid flows of smooth inelastic spheres. Unfortunately as in the classical Chapman–Enskog expansion for elastic spheres any truncation of the expansion beyond Navier–Stokes order (n=1) will possess unphysical instabilities. This paper uses the method of approximate summation of the Chapman–Enskog expansion presented by the author (in press, Arch. Rational Mech. Anal.) to eliminate these instabilities.