Lattice Boltzmann Method without Invoking the M << 1 Assumption

Abstract

When a Maxwellian distribution is assumed for the distribution function in the BGK-type modelled BE, it will give rise to the Euler equations if it is the first-order approximation in the Chapman-Enskog method. Then the second-order equations will yield the N-S equations. Most LBM developed to date are formulated based on the second-order equations. Consequently, the assumption of a flow Mach number M << 1 is inherent in this formulation. This approach creates an unnecessary restriction on the LBM that should be avoided if possible. An alternative approach is to formulate a new LBM by considering an equilibrium distribution function where the first-order approximations give rise to the N-S equations. Adopting this approach, a new LBM has been formulated. This new LBM gives reliable results when applied to simulate aeroacoustics, incompressible flows, and compressible flows with and without shocks. Good agreement with measurements and numerical data derived from DAS/DNA calculations is obtained.