Lattice Boltzmann BGK simulation of nonlinear sound waves: the development of a shock front

James Buick, C. L. Buckley, C. A. Greated , J. Gilbert

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    Abstract

    The application of the lattice Boltzmann model to simulating nonlinear propagative acoustic waves is considered. The lattice Boltzmann model, and its application to the study of nonlinear sound propagation, are discussed. Lattice Boltzmann simulations of the development of a shock front are performed when a sound wave is emitted from a high-amplitude sinusoidal source. For a number of parameters, representing different physical situations, the wave 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 propagation at high Reynolds number is considered. These results suggest that the lattice Boltzmann model is a useful technique for studying a range of problems in nonlinear acoustics.
    Original languageEnglish
    Pages (from-to)3917-3928
    JournalJournal of Physics A: Mathematical and General
    Volume33
    Issue number21
    DOIs
    Publication statusPublished - 2 Jun 2000

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