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A polynomial expansion procedure and an analytical discrete-ordinates method are used to solve a collection of basic flow problems based on a rigorous version of the linearized Boltzmann equation for rigid-sphere interactions. In particular, two half-space problems, Kramers and thermal creep, and three problems defined by flow in a plane-parallel channel, Poiseuille, thermalcreep and Couette flow, are solved (essentially) analytically in terms of a modern version of the discrete-ordinates method. The developed algorithms are implemented for general values of the accommodation coefficient to yield numerical results that can be considered a new standard of reference.

A version of the discrete-ordinates method is used to solve in a unified manner some classical flow problems based on the Bhatnagar, Gross and Krook model in the theory of rarefiedgas dynamics. In particular, the thermal-creep problem and the viscous-slip (Kramers') problem are solved for the case of a semi-infinite medium, and the Poiseuille-flow problem, the Couetteflow problem and the thermal-creep problem are all solved for a wide range of the Knudsen number.

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