Numerical solutions of the Boltzmann-BGK equation for oscillatory gas flows

© 2014 Dr. Ying Wan YapRecent developments in nano- and micro- technology have led to fabrication of mechanical devices that resonate at ultra-high frequency (100 MHz -- 100 GHz), with potential applications in a wide range of areas including environmental sensing and atomically resolved mass measurement. Such gas flows are strongly nonequilibrium, with the mean free path of the gas comparable to the device dimensions and oscillation frequencies comparable to the interparticle collision frequency of the gas. This invalidates use of the standard Navier-Stokes equations and conventional no-slip condition governing fluid flow. For such gas flows, the kinetic theory of gases provides a more rigorous theoretical framework. Derived from a statistical treatment of the gas, the Boltzmann equation for a dilute gas is a conservation equation for the mass distribution function. Due to the general complexity of the collision integral, the Bhatnagar-Gross-Krook (BGK) kinetic model is often used as a simplified approximation for interparticle collisions. In this thesis, we derive high accuracy numerical solutions of the linearised Boltzmann-BGK equation for two canonical flow problems. A comprehensive set of high accuracy solutions are obtained for unidirectional steady and unsteady Couette flows. The method of solution is then extended to a three-dimensional oscillatory flow around a sphere. While solutions for steady flow past a sphere has been reported, oscillatory flow is yet to be investigated. These numerical solutions are of particular value for the benchmarking and validation of approximate analytical and numerical methods based on the BGK model. We demonstrate this application by assessing the performance of the lattice Boltzmann method and matched asymptotic solutions recently developed for oscillatory flows