An accurate two-stream moment method for kinetic boundary layer problems of linear kinetic equations

Abstract

The authors develop a method for solving 1D kinetic boundary layer problems for linear equations that uses separate Hermite moment expansions in the velocity variable for particles moving towards and away from a plane wall. This so-called two-stream method is tested for two especially simple kinetic equations, the linear BGK equation and the Klein-Kramers equation, the kinetic equation for Brownian particles. For both of these equations, extensive exact information is available for two simple boundary layer problems, the Milne and the albedo problem. A comparison of these exact results with those obtained with this version of the two-stream moment method shows that the accuracy obtainable by this method exceeds that of earlier methods by several orders of magnitude. In particular, the method allows them to obtain accurate results not only for the moments of the distribution function, but also for the distribution function itself.