Abstract
The Lattice Boltzmann Method (LBM)is used to study the propagation of high amplitude progressive sound wave radiated from a piston in a duct. The discretised Boltzmann equation for the 2D21V thermal BGK model is solved using a second-order Runge-Kutta scheme in time and a fifth-order upwind difference scheme in space. The formation of a shock front and the development of saw tooth waves are simulated for the dimensionless distance x^^- up to 3. The Fourier component amplitudes of computed waveforms are obtained. The simulations are compared with the solution of Burgers' equation, The results show good agreement with Burgers' equation for non-linearity factor Γ〜O(1). For Γ>>1 i.e. when the effect of non-linearity is strong relative to thermo-viscous dissipation, the feature describing the occurrence of acoustic streaming in the direction of wave propagation after shock formation is observed. These results suggest that the LBM is useful for studying a wider range of nonlinear acoustical problems than Burgers' equation.
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