Commun. Comput. Phys., 13 (2013), pp. 671-684.


Sound Propagation Properties of the Discrete-Velocity Boltzmann Equation

Erlend Magnus Viggen 1*

1 Department of Electronics and Telecommunications, Norwegian University of Science and Technology (NTNU), 7034 Trondheim, Norway.

Received 28 October 2011; Accepted (in revised version) 2 February 2012
Available online 29 August 2012
doi:10.4208/cicp.271011.020212s

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.

AMS subject classifications: 76Q05, 76P05

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Key words: Lattice Boltzmann method, discrete-velocity Boltzmann equation, sound propagation, computational aeroacoustics.

*Corresponding author.
Email: erlend.viggen@ntnu.no (E. M. Viggen)
 

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