As the numerical resolution is increased and the discretization error decreases, the lattice Boltzmann method tends towards the discrete-velocity Boltzmann equation (DVBE). An expression for the propagation properties of plane sound waves is found for this equation. This expression is compared to similar ones from the Navier-Stokes and Burnett models, and is found to be closest to the latter. The anisotropy of sound propagation with the DVBE is examined using a two-dimensional velocity set. It is found that both the anisotropy and the deviation between the models is negligible if the Knudsen number is less than 1 by at least an order of magnitude.

}, issn = {1991-7120}, doi = {https://doi.org/10.4208/cicp.271011.020212s}, url = {https://global-sci.com/article/80641/sound-propagation-properties-of-the-discrete-velocity-boltzmann-equation} }