Study of rarefied shear flow by the discrete velocity method

Abstract

The application of a simple discrete velocity model to low Mach number Couette and Rayleigh flow is investigated. In the model, the molecular velocities are restricted to a finite set and in this study only eight equal speed velocities are allowed. The Boltzmann equation is reduced by this approximation to a set of coupled differential equations which can be solved in closed form. The fluid velocity and shear stress in Couette flow are in approximate accord with those of Wang Chang & Uhlenbeck (1954) and of Lees (1959) over the complete range of Knudsen number. Similarly, the Rayleigh flow solution is remarkably like those found by other investigators using moment methods.