Finite Difference Lattice Boltzmann Method Applied to Acoustic-Scattering Problems

This paper reports on an attempt to simulate acoustic waves scattering using a finite-difference lattice Boltzmann method based on an alternative lattice equilibrium particle distribution function constructed for compressible thermal fluids. The studies focus on acoustics scattering by a zero-circulation vortex and by an isolated thermal source with no heat gain/loss. Two limiting cases of each type of scattering are examined; one is the case of an incoming acoustic wave with a short wavelength, and the other has a relatively long wavelength compared with the characteristic dimension of the obstacle. These scattering problems have been treated previously using a conventional lattice Boltzmann method and a gas-kinetic scheme. The results showed that these methods were only able to simulate the shortwavelength limit casewith fair accuracy for the two types of acoustics scattering considered. Because the present approach is able to recover the compressible Navier–Stokes equations with correct fluid properties, the finite-difference solution of the proposed alternative modeled lattice Boltzmann equation allows the limiting cases of the acoustics scattering problems to be calculated without numerical instability. The results thus obtained are in agreement either with analysis or with results obtained from direct aeroacoustics simulations employing the compressible Navier–Stokes equations. Nomenclature c = speed of soun