Reconsideration of Planar Couette Flows Using the Statistical Bhatnagar-Gross-Krook Approach

Abstract

DOI: 10.2514/1.44409 Anumberofresearchershaveconsideredtransitional-flowgasdynamicapproachestothewell-knowncaseof 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 ellipsoidalstatisticalBhatnagar–Gross–Krookmethods.ThepaperwillpresentbenchmarkdirectsimulationMonte Carlo solutions, by which analytic and Bhatnagar–Gross–Krook/ellipsoidal statistical Bhatnagar–Gross–Krook simulationsmaybecomparedfor flowvelocities,temperatures,heat fluxes,andshearingcoefficients.Thedifferences 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 numericallymoreefficientthanthedirectsimulationMonteCarlomethodfora flowconditionthatispresentlyatthe comfort-levellimitfordirectsimulationMonteCarlocomputations.Finally,itwillbeshownthatananalyticsolution for incompressible, argon, transitional flow (Knudsennumber 0:01) remains valid beyond the applicability ranges suggested in the original work.