Shear-driven micro/nano flows simulation using Fokker Planck approach: Investigating accuracy and efficiency

Abstract

A detailed study on the performance and accuracy of the Fokker Planck (FP) approach in treating shear driven flows over a wide range of Knudsen numbers and Mach numbers at subsonic and supersonic regimes is considered. One-dimensional Couette flow and the two-dimensional cavity problem are considered. The FP method is evaluated in the Couette flow at a subsonic Mach number of 0.16 (Uw = 50 m/s) and at the supersonic Mach number of 3.1 (Uw = 1000 m/s), where Knudsen numbers range from 0.005 to 1. Correspondingly, the cavity flow is investigated at a wall Mach number of 0.31 (Uw = 100 m/s) and wall Mach number of 0.93 (Uw = 300 m/s) at Knudsen numbers ranging from 0.05 to 20. Interestingly, the results show that by increasing the wall velocity and Knudsen numbers, the accuracy of the FP approach increases in treating the cavity flow. In addition to the standard Knudsen number, we show that gradient length Knudsen number, KnGL, should be considered to determine the range of accuracy of the FP scheme. The latter depends on the strength of the center vortex of the cavity diminishing at higher rarefied conditions. The results demonstrate that the computational efficiency of the FP approach enhances at higher lid velocity.