Elementary solutions of the linearized gas-dynamics boltzmann equation and their application to the slip-flow problem

Abstract

A new method for treating problems involving the gas-dynamics Boltzmann equation is developed. It is analogous to the Case method, developed for the solution of the neutron transport equation. The elementary solutions have separated variables and are shown to have properties similar to the Case's ones, with some notable exceptions. The model of Gross, Bhatnagar, and Krook is used. The paper is devoted to problems at a constant temperature; the extension of the method to problems with a temperature gradient will be considered in a subsequent paper. Besides the general theory of pure shear problems in unidimensional plane geometry, a solution of the slip-flow problem is given as an illustration. An analytical expression of the slip-flow coefficient, particularly suitable to a numerical calculation, is this obtained.