Continuum equations in the dynamics of rarefied gases

Abstract

A procedure is given for translating boundary-value problems of gas dynamics from microscopic form into approximately equivalent continuum form. The continuum formulations involve state-variables that are either half-space moments, or complete moments of the molecular distribution functions. Moment equations derived from the kinetic equations are reduced to a determinate set by representing the distribution functions as sums of ‘modified Maxwellian functions based on various characteristic temperatures and velocities’. The particular choice of such a representation depends on the Knudsen number and on the nature of the microscopic boundary conditions.