Lattice Boltzmann BGK simulation of nonlinear sound waves: The developmentof a shock front

The application of the lattice Boltzmann model to simulating nonlinear prop agative acoustic waves is considered. The lattice Boltzmann model, and its application to the study of nonlinear sound propagation, are discussed. Lat tice Boltzmann simulations of the development of a shock front are performe d when a sound wave is emitted from a high-amplitude sinusoidal source. For a number of parameters, representing different physical situations, the wa ve development is compared with inviscid shock theory and with the solution of Burgers' equation for a fully viscous fluid. The simulations show good agreement with Burgers' equation and with the inviscid theory when propagat ion at high Reynolds number is considered. These results suggest that the l attice Boltzmann model is a useful technique for studying a range of proble ms in nonlinear acoustics.