Asymptotic theory of the Boltzmann system, for a steady flow of a slightlyrarefied gas with a finite Mach number: General theory

A steady rarefied gas how with Mach number of the order of unity around a b ody or bodies is considered. The general behaviour of the gas for small Knu dsen numbers is studied by asymptotic analysis of the boundary-value proble m of the Boltzmann equation for a general domain. The effect of gas rarefac tion (or Knudsen number) is expressed as a power series of the square root of the Knudsen number of the system. A series of fluid-dynamic type equatio ns and their associated boundary conditions that determine the component fu nctions of the expansion of the density, flow velocity, and temperature of the gas is obtained by the analysis. The equations up to the order of the s quare root, of the Knudsen number do not contain non-Navier-Stokes stress a nd heat flow, which differs from the claim by Darrozes (in Rarefied Gas Dyn amics, Academic Press, New York, 1969). The contributions up to this order, except in the Knudsen layer, are included in the system of the Wavier-Stok es equations and the slip boundary conditions consisting of tangential velo city slip due to the shear of flow and temperature jump due to the temperat ure gradient normal to the boundary. (C) 2000 Editions scientifiques et med icales Elsevier SAS.