An attempt to calculate acoustic directivity using LBM

A lattice Boltzmann method (LBM) that can recover the specific heat ratio, the sound speed and the first coefficient of viscosity correctly has been proposed for one-step aeroacoustic simulation because the method only involves the solution of one scalar equation and is relatively simple. The proposed LBM has been validated against direct numerical simulation (DNS) results obtained by solving the unsteady compressible Navier-Stokes equations using a finite difference scheme. The comparisons showed that the proposed LBM and the DNS give identical results on propagation of acoustic, entropy and vortex pulses. In order to demonstrate that the proposed LBM is truly applicable to one-step aeroacoustic problems, correct replication of the interaction between the aerodynamic and acoustic field has to be proven. The present paper reports on an attempt of this problem. The first step is to show that the LBM can simulate plane sinusoidal wave propagation in quiescent fluid and that the LBM result is truly isotropic with no distortion in sound propagation. The second step is to compute sound scattering of high frequency acoustics wave with length λ = 2 from a zero circulation vortex. The LBM result is compared with DNS simulations.