Properties of the Lattice Boltzmann Method for Acoustics

TLDR

The study uses numerical simulations to investigate the fundamental acoustic properties of the Lattice–Boltzmann method, focusing on planar wave propagation and resolution‑dependent dissipation and dispersion. The authors analyze temporal decay of standing plane waves and spatial decay of Gaussian acoustic pulses in periodic domains, deriving theoretical dispersion relations from linearized Navier–Stokes equations and examining dissipation and dispersion with and without turbulence modeling. The results confirm that the Lattice–Boltzmann method exhibits low dispersion and dissipation, accurately reproducing time‑explicit acoustic phenomena.

Abstract

Numerical simulations are performed to investigate the fundamental acoustics properties of the Lattice–Boltzmann method. The propagation of planar acoustic waves is studied to determine the resolution dependence of numerical dissipation and dispersion. The two setups considered correspond to the temporal decay of a standing plane wave in a periodic domain, and the spatial decay of a propagating planar acoustic pulse of Gaussian shape. Theoretical dispersion relations are obtained from the corresponding temporal and spatial analyses of the linearized Navier–Stokes equations. Comparison of theoretical and numerical predictions show good agreement and demonstrate the low dispersive and dissipative capabilities the Lattice–Boltzmann method. The analysis is performed with and without turbulence modeling, and the changes in dissipation and dispersion are discussed. Overall, the results show that the Lattice–Boltzmann method can accurately reproduce time-explicit acoustic phenomena.