Constitutive Relations for Monatomic Gases¶Based on a¶Generalized Rational Approximation¶to the Sum of the Chapman-Enskog Expansion

Abstract:

The classical Chapman-Enskog expansions for the pressure deviator P and heat flux q provide a natural bridge between the kinetic description of gas dynamics as given by the Boltzmann equation and continuum mechanics as given by the balance laws of mass, momentum, and energy supplemented by the expansions for P and q. Truncation of these expansions beyond first (Navier-Stokes) order yields instability of the rest state and is inconsistent with thermodynamics. This paper shows how an approximate sum of the Chapman-Enskog expansion via generalized rational approximation eliminates the instability paradox and yields gas dynamics consistent with a generalized Clausius-Duhem inequality.