Reconsideration of planar couette flows using the statistical Bhatnagar-Gross-Krook approach

A number of researchers have considered transitional-flow gas dynamic approaches to the well-known case of flow through moving parallel plates. The papers consider different initial conditions and different aspects of the problem and, in some cases, reach conclusions that will be shown to be contradictory to careful numerical simulations. The purpose of this paper is to reexamine some of these key works on planar Couette flow, one of the most fundamental fluid-dynamics problems, particularly with respect to the calibration of the statistical Bhatnagar-Gross-Krook and ellipsoidal statistical Bhatnagar-Gross-Krook methods. The paper will present benchmark direct simulation Monte Carlo solutions, by which analytic and Bhatnagar-Gross-Krook/ ellipsoidal statistical Bhatnagar-Gross-Krook simulations may be compared for flow velocities, temperatures, heat fluxes, and shearing coefficients. The differences among the solutions obtained by the direct simulation Monte Carlo, Bhatnagar-Gross-Krook, and ellipsoidal statistical Bhatnagar-Gross-Krook methods will be examined from a microscopic point of view, and the statistical Bhatnagar-Gross-Krook and ellipsoidal statistical Bhatnagar-Gross-Krook methods will be shown to be numerically more efficient than the direct simulation Monte Carlo method for a flow condition that is presently at the comfort-level limit for direct simulation Monte Carlo computations. Finally, it will be shown that an analytic solution for incompressible, argon, transitional flow (Knudsen number = 0:01) remains valid beyond the applicability ranges suggested in the original work.