Alternatives to the Euler and Navier–Stokes equations for monatomic gases

Abstract

The Chapman–Enskog approximation scheme is not uniformly convergent because it does not approximate sufficiently the behavior of molecules in the high-speed tail of a distribution. Asymptotic analysis of the binary collision term in the Boltzmann equation is used to show that collisions involving high-speed molecules can redistribute molecules within an energy level more easily than between levels. Chapman–Enskog theory is reformulated by assuming near equilibrium, only within each energy level, instead of over all energy levels.