Lattice Boltzmann method and its applications in engineering thermophysics

The lattice Boltzmann method (LBM), a mesoscopic method between the molecular dynamics method and the conventional numerical methods, has been developed into a very efficient numerical alternative in the past two decades. Unlike conventional numerical methods, the kinetic theory based LBM simulates fluid flows by tracking the evolution of the particle distribution function, and then accumulates the distribution to obtain macroscopic averaged properties. In this article we review some work on LBM applications in engineering thermophysics: (1) brief introduction to the development of the LBM; (2) fundamental theory of LBM including the Boltzmann equation, Maxwell distribution function, Boltzmann-BGK equation, and the lattice Boltzmann-BGK equation; (3) lattice Boltzmann models for compressible flows and non-equilibrium gas flows, bounce back-specular-reflection boundary scheme for microscale gaseous flows, the mass modified outlet boundary scheme for fully developed flows, and an implicit-explicit finite-difference-based LBM; and (4) applications of the LBM to oscillating flow, compressible flow, porous media flow, non-equilibrium flow, and gas resonant oscillating flow.