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

Abstract

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. © 2001 Academic Press.