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Abstract

As the numerical resolution is increased and the discretisation 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.
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... An application of the LBM to propagation of plane sound waves is described in Ref. [11]. An extensive study of application of the LBM in acoustics has been performed by Viggen [12][13][14][15][16]. ...
... With the standard LBM, only viscous effects are included. Moreover, the LBM is not stable for small values of the viscosity, so the true dissipation of sound waves in air cannot be reproduced with the LBM [14,15]. ...
Article
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Propagation of sound waves in air can be considered as a special case of fluid dynamics. Consequently, the lattice Boltzmann method (LBM) for fluid flow can be used for simulating sound propagation. In this article application of the LBM to sound propagation is illustrated for various cases: free-field propagation, propagation over porous and non-porous ground, propagation over a noise barrier, and propagation in an atmosphere with wind. LBM results are compared with solutions of the equations of acoustics. It is found that the LBM works well for sound waves, but dissipation of sound waves with the LBM is generally much larger than real dissipation of sound waves in air. To circumvent this problem it is proposed here to use the LBM for assessing the excess sound level, i.e. the difference between the sound level and the free-field sound level. The effect of dissipation on the excess sound level is much smaller than the effect on the sound level, so the LBM can be used to estimate the excess sound level for a non-dissipative atmosphere, which is a useful quantity in atmospheric acoustics. To reduce dissipation in an LBM simulation two approaches are considered: i) reduction of the kinematic viscosity and ii) reduction of the lattice spacing.
Article
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Chapter
After reading this chapter, you will understand the fundamentals of sound propagation in a viscous fluid as they apply to lattice Boltzmann simulations, and you will know why sound waves in these simulations do not necessarily propagate according to the “speed of sound” lattice constant. You will have insight into why sound waves can appear spontaneously in lattice Boltzmann simulations and know how to create sound waves artificially in your simulations. Additionally, you will know about special boundary conditions that minimise the reflection of sound waves back into the system, allowing you to avoid reflected sound waves polluting the simulation results.
Article
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Thesis
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Article
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Article
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Article
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Article
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Article
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