Two half-space problems based on a synthetic-kernel model of the linearized Boltzmann equation

An analytical discrete-ordinates method is used to solve two basic half-space problems based on a new synthetic-kernel model of the linearized Boltzmann equation. In particular, Kramers’ problem and the half-space problem of thermal creep, both basic to the general area of rarefied-gas dynamics, are defined by model equations that are solved (essentially) analytically in terms of a modern version of the discrete-ordinates method. The developed algorithms are implemented to yield numerical results for the slip coefficients and the velocity and heat-flow profiles that compare well with solutions derived from much more computationally intensive techniques.