Application Of A Lattice Boltzmann Method On Non-Uniform Meshes For Simulation Of Micro Flows

In the recent past, the lattice Boltzmann method (LBM) has received much attention in science and engineering as a potential computational tool for solving a large class of problems such as flows in micro-geometries. In this work, a compressible LBM in conjunction with the explicit Taylor series expansion and least square based lattice Boltzmann method (TLLBM) is used to simulate two-dimensional micro flows. TLLBM is based on the standard LBM with an introduction of the Taylor series expansion and the least squares approach. The final equation is an explicit form and essentially has no restriction on mesh structure and lattice model. To validate the method, both lid driven micro cavity flow and micro channel flow at different Knudsen numbers are considered. Numerical results obtained by this method agree very well with available data in the literature.