Sound Propagation Properties of the Discrete-Velocity Boltzmann Equation (Communications in Computational Physics, 2020)
As the numerical resolution is increased and the discretization error decreases, the lattice Boltzmann method tends towards the discrete-velocity Boltzmannequation (DVBE). An expression for the propagation properties of plane sound wavesis 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 ofsound 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 negligibleif the Knudsen number is less than 1 by at least an order of magnitude.