High accuracy numerical solutions of the Boltzmann Bhatnagar-Gross-Krook equation for steady and oscillatory Couette flows

Abstract

Modeling gas flows generated by micro- and nano-devices often requires the use of kinetic theory. To facilitate implementation, various approximate formulations have been proposed based on the Bhatnagar-Gross-Krook (BGK) kinetic model, including most recently, the lattice Boltzmann (LB) method. While there exists a comprehensive numerical data set for the hard sphere linearized Boltzmann equation for steady Couette flow, no such set of data is available for the Boltzmann-BGK equation. The purpose of this article is to present a high accuracy data set for the linearized Boltzmann-BGK equation over the full range of Knudsen numbers and normalized oscillation frequencies – this encompasses both steady and unsteady Couette flows. This data set is expected to be of particular value in the benchmarking and validation of computational methods such as the LB method and other approaches based on the Boltzmann-BGK equation.