In this paper, the lattice Boltzmann method is used to study the acoustic waves propagation inside a differentially heated square enclosure filled with air. The waves are generated by a point sound source located at the center of this cavity. The main aim of this simulation is to simulate the interaction between the thermal convection and the propagation of these acoustic waves. The results have been validated with those obtained in the literature and show that the effect of natural convection on the acoustic waves propagation is almost negligible for low Rayleigh numbers (Ra ≤ 10⁴), which begins to appear when the Rayleigh number begins to become important (Ra ≥ 10⁵) and it becomes considerable for large Rayleigh numbers (Ra ≥ 10⁶) where the thermal convection is important.

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.

This research concerns the quality of heat transfer across a two-dimensional backwards-facing step in the presence of vertical or inclined partitions in a rectangular channel. Convective and conjugate heat transfer input using constant temperature and heat flux were successfully achieved for low Reynolds number values. The actual code based on the double multiple relaxation time of the lattice Boltzmann method was employed to model numerically the physical problems related to the fluid flow and heat transfer, where the obtained results had a good agreement with previous experimental research. During this study, parametric variations were carried out according to the inclination and position of the partitions, as well as the thermal conductivity ratio in the case of the conjugate heat transfer problem. The numerical results show that the involvement of the partitions and the thermal conductivity ratio has a significant effect on the fluid flow and heat transfer. This impact controls the evolution of local Nusselt number, bulk temperature, and skin friction coefficient. The improvement of heat transfer is remarkable by the introduction of vertical or inclined partitions such that the quality of heat exchange reaches about 7%. While the presence of two inclined partitions increases the heat transfer by about 6% in case of constant temperature of studied hot wall. The implementation of constant heat flux for the hot wall increases the quality of heat transfer by about 9%-10% by the presence of inclined or vertical walls, 11%-13% with double inclined partitions.