Numerical analysis of the shear and thermal creep flows of a rarefied gas over a plane wall on the basis of the linearized Boltzmann equation for hard-sphere molecules

Abstract

Shear flow and thermal creep flow (flow induced by the temperature gradient along the boundary wall) of a rarefied gas over a plane wall are considered on the basis of the linearized Boltzmann equation for hard-sphere molecules and diffuse reflection boundary condition. These fundamental rarefied gas dynamic problems, typical half-space boundary-value problems of the linearized Boltzmann equation, are analyzed numerically by the finite-difference method developed recently by the authors, and the velocity distribution functions, as well as the macroscopic variables, are obtained with good accuracy. From the results, the shear and thermal creep slip coefficients and their associated Knudsen layers of a slightly rarefied gas flow past a body are derived. The results for the slip coefficients and Knudsen layers are compared with experimental data and various results by the Boltzmann–Krook–Welander (BKW) equation, the modified BKW equation, and a direct simulation method.