Three-Dimensional Lattice Boltzmann Model for Acoustic Waves Emitted by a Source

Abstract

The present paper implements the lattice Boltzmann method (LBM) to simulate the emission and propagation of sound waves in three-dimensional (3D) situations, with the point source technique used for wave emission. The 3D numerical model is exercised on a benchmark problem, which is the simulation of the lid-driven cavity flow. Tests are then proposed on acoustic situations. The numerical results are first confronted with analytical solutions in the case of spherical waves emitted by a single point source at the center of a cavity. In view of acoustic streaming applications, we then study the case where the waves are emitted from a circular sound source placed at the center of the left boundary of a three-dimensional cavity filled with water. With the circular source discretized as a set of point sources, we can simulate the wave propagation in 3D and calculate the sound pressure amplitude in the cavity. Tests using different emission conditions and LBM relaxation times finally allow us to get good comparisons with analytical expressions of the pressure amplitude along the source axis, highlighting the performance of the lattice Boltzmann simulations in acoustics.

Three‐dimensional numerical study of heat transfer enhancement by sound waves using mesoscopic and macroscopic approaches

“…The studies carried out in the literature 20,21 show that the D3Q19 model is more powerful than the other two models in terms of reliability and computational efficiency. This model was used in our previous work 22 to study the sound waves generated by a circular source located at the center of the left wall of a 3D cavity filled with water. It showed an excellent numerical performance.…”

“…60 The second is an indirect tool. It begins with the computation of the acoustic force from the calculation of the average acoustic pressure or intensity, 22 and then it introduces this force into the LBM numerical code to obtain the streaming. The study of these two methodologies and their comparison are the subjects of our future work on the 3D simulation of acoustic streaming with the LBM-MRT approach.…”

“…Numerically, the discretized form of the Boltzmann equation is used to describe the evolution of the distribution function $${f}_{i}({x}_{i},t)$$ 1,22–26 : $$${f}_{i}({x}_{i}+{c}_{i}\Delta t,t+\Delta t)={f}_{i}({x}_{i},t)+{{\rm{\Omega }}}_{i}.$$$…”

“…The second technique is the acoustic point source method. 22,23,[38][39][40] Its principle is to vibrate the pressure, density, or velocity around their equilibrium position using a sinusoidal function based on the linear wave approximation. This approximation allows one to write 22,41…”

“…In our previous studies, 22,23,40,42 the condition based on the vibration of the density is well discussed and shows good accuracy, in particular when the waves are emitted by a single point source. However, for a vibrating surface, it makes more sense to put the condition on the velocity than on the density to generate the waves.…”