Constructive solution of the linearized Boltzmann equation: Vector BGK model

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Abstract
The temperature-density equation, a system of coupled, integro-differential equations derived from the Boltzmann equation by applying the BGK model, is studied. Full-range and half-range expansions are obtained by applying a modified version of the Larsen-Habetler resolvent integration technique. This development extends previous results by enlarging the class of expandable functions and has the added advantages of rigor and simplicity. Application is illustrated by analyzing the temperature jump problem. For the case of arbitrary accomodation an integral equation for the surface density is reported which has not previously appeared in the literature. This equation is shown to have a unique solution except perhaps at a finite number of values of the accomodation coefficient.

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