A deterministic parallel algorithm to solve a model Boltzmann equation (BGK)

This paper documents the use of a massively parallel computer, specifically the Connection Machine, to solve the Boltzmann equation to model one-dimensional shock wave structure. The Bhatnagar-Gross-Krook (BGK) model for the collision term combined with a finite difference scheme was used to model the flow. This collision term requires accurate knowledge of the density, temperature and mean velocity. Great care must be taken in their calculation to insure conservation, which proved to be the most difficult part. The algorithm, however, is well suited to the Connection Machine and accurate results were obtained with great efficiency. The code was written in a general form to be readily extended to model other flows, including three-dimensional flows.