Piecewise continuous partition function method in the theory of wave   perturbations of inhomogeneous gas
  The problem of wave disturbance propagation in rarefied gas in gravity field is explored. The system of hydrodynamic-type equations for a stratified gas in gravity field is derived from BGK equation by method of piecewise continuous partition function. The obtained system of the equations generalizes the Navier-Stokes at arbitrary density (Knudsen numbers). The verification of the model is made for a limiting case of a homogeneous medium. Results are in the good agreement with experiment and former theories at arbitrary Knudsen numbers. 
D.A. Vereshchagin, S.B. Leble, M.A. Solovchuk