Study Of Lattice Boltzmann Method And Its Application On Microflows

As the development of science and technology, researches on Micro-Electro Mechanical System (MEMS) presented to be a unheard rapid tendency, and was extended to industrial applications widely.At present situation, the manufacture technologies of MEMS have achieved great advancement, but the physical mechanisms researches on MEMS have been lagged far behind. This problem obstructs further optimization, improvement and popularization of MEMS severely. As one of those physical mechanisms, flows in micro-nano channel are the fundament of other subjects. Since the specialness of flows, especially the micro-flows, theoretical or experimental methods are restricted hugely. As the best choice, numerical simulation was chosen by most researchers. For the unique mesoscopic standpoint, Boltzmann equation attracted more and more attention. As well, it was considered as the theoretical base of numerical simulation in this paper.In this paper, elementary studies on Lattice Boltzmann method, which origins from Boltzmann equation, and its applications on micro flows were done. Fist, Boltzmann equation and its relationship with Navier-Stokes equations were derived in different manners, further more, deduced to Lattice Boltzmann method, and followed with verification via numerical simulation. Second, aiming at the shortages of Lattice Boltzmann method, finite difference based Lattice Boltzmann method (FDLBM) was applied to further studies, and the stability of FDLBM was analyzed. Third, in order to improve FDLBM's ability against stiffness, the numerical techniques developed in traditional CFD have been introduced, and its robustness has been demonstrated via numerical test. Finally, the improved numerical method was applied to the study of micro flows, its ability on micro flows simulation was verified.Via investigations and numerical analysis, we concluded that, as a new numerical method, Lattice Boltzmann method is an effective numerical tool for flows simulation. But, as far as it goes, Lattice Boltzmann method is essentially a Navier-Stokes solver, and can not describe Boltzmann equation sufficiently. So, its application on micro flows will encounter the same problems, as any other Navier-Stokes solvers. However, for the reason that Lattice Boltzmann method is based on Boltzmann equation, it is anticipated that Lattice Boltzmann method will be a promising method.