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.

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The objective of this research is to study the fluid flow control allowing the reduction of aerodynamic drag around a square cylinder using two parallel partitions placed downstream of the cylinder using the lattice Boltzmann method with multiple relaxation times (MRT-LBM). In contrast to several existing investigations in the literature that study either the effect of position or the effect of length of a single horizontal or vertical plate, this work presents a numerical study on the effect of Reynolds number (Re), horizontal position (g), vertical position (a), and length (Lp) of the two control partitions. Therefore, this work will be considered as an assembly of several results presented in a single work. Indeed, the Reynolds numbers are selected from 20 to 300, the gap spacing (0 ≤ g ≤ 13), the vertical positions (0 ≤ a ≤ 0.8d), and the lengths of partitions (1d ≤  Lp ≤  5d). To identify the different changes appearing in the flow and forces, we have conducted in this study a detailed analysis of velocity contours, lift and drag coefficients, and the root-mean-square value of the lift coefficient. The obtained results revealed three different flow regimes as the gap spacing was varied. Namely, the extended body regime for 0 ≤ g ≤ 3.9, the attachment flow regime for 4 ≤ g ≤ 5.5, and the completely developed flow regime for 6 ≤ g ≤ 13. A maximal percentage reduction in drag coefficient equal to 12.5%, is given at the critical gap spacing (gcr = 3.9). Also, at the length of the critical partition (Lpcr = 3d), a Cd reduction percentage of 12.95% was found in comparison with the case without control. Moreover, the position of the optimal partition was found to be equal to 0.8d i.e. one is placed on the top edge of the square cylinder and the second one is placed on the bottom edge. The maximum value of the lift coefficient is reached for a plate length Lp = 2d when the plates are placed at a distance g = 4. On the other hand, this coefficient has almost the same mean value for all spacings between the two plates. Similarly, the root means the square value of the lift coefficient (Clrms) admits zero values for low Reynolds numbers and then increases slightly until it reaches its maximum for Re = 300.