Application of the lattice Boltzmann method to the study of ultrasound propagation and acoustic streaming in three-dimensional cavities: advantages and limitations

The paper presents a three-dimensional numerical study of the acoustic streaming induced by the dissipation of ultrasounds during their propagation in the air. The waves are generated by a circular acoustic source positioned at the center of the left wall of a parallelepipedic cavity. The simulations are performed with the lattice Boltzmann method associated with the D3Q19 multiple relaxation time model. A validation of this model is first performed by comparing the numerical and analytical acoustic intensities along the central axis of the acoustic source. The main objective of this study is to use two different methods to calculate the acoustic streaming flow. The first method is the direct calculation of the mean velocity fields as the mean values of the instantaneous velocities. The second method is an indirect technique, which first calculates the acoustic streaming force and then injects this force into the numerical code to produce the streaming. A comparison between the results obtained by the two methods was carried out and a good agreement was found between them. These different investigations, rather new in three-dimensional configurations, have allowed us to discuss the advantages and limitations of the lattice Boltzmann approach to simulate real situations of wave propagation and acoustic streaming.