A Review of Lattice Boltzmann Models for Compressible Flows

Abstract

This chapter reviews the Lattice Boltzmann method (LBM) for compressible flows. The LBM is a relatively new numerical approach for simulating complex flow and transport phenomena in cases where a direct solution of the Navier-Stokes equations is impractical or undesirable. Unlike the conventional computational fluid dynamics (CFD) method based on macroscopic continuum equations, the LBM uses a microscopic equation—the Boltzmann equation—to determine macroscopic fluid dynamics. The LBM is flexible, has broad applicability, and may be easily adapted for parallel computing. The LBM originated from a Boolean model known as the lattice gas automata (LGA). The LB model is applied to various physical problems, such as single component hydrodynamics, multiphase, and multi-component fluid flows, magneto hydrodynamics, reaction-diffusion systems, flows through porous media, and other complex systems at small Mach numbers. Models that retain the conventional small velocity set and equilibrium distribution function generally still suffer limitations of small Mach numbers. Most of the new compressible flow models have been only applied to simple wave problems, with the exception of the adaptive velocity model by the present authors.