Simulation of microflows using the lattice Boltzmann method on nonuniform meshes

In the recent past, the lattice Boltzmann method (LBM) has attracted considerable attention in science and engineering as a potential computational tool for solving a large class of problems such as flows in microgeometries. In this work, a compressible LBM in conjunction with the explicit Taylor-series expansion and least squares-based lattice Boltzmann method (TLLBM) is used to simulate two-dimensional microflows. The TLLBM is based on the standard LBM with an introduction of the Taylor-series expansion and least squares approach. The final equation is in an explicit form and essentially has no restriction on mesh structure and lattice model. To validate the method, both a lid-driven microcavity flow and microchannel flow at different Knudsen numbers are considered. Numerical results obtained by this method agree very well with the data available in the literature. © 2012 by Begell House, Inc.