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

This paper implements the lattice Boltzmann method to simulate the propagation of sound waves in three dimensions. The numerical model is exercised on the lid-driven cavity flow. Tests are then proposed on acoustic situations. The results are first confronted with analytical solutions of the spherical waves emitted by a single point source inside a cubic cavity. Then, we studied the case where the waves are emitted from a circular sound source placed at the center of the left boundary of a parallelepipedic cavity filled with water. With the circular source discretized as a set of point sources, we were able to simulate the wave propagation in 3D and calculate the sound pressure amplitude. Tests using different emission conditions and LBM relaxation times finally allowed 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.