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Sound Propagation Properties of the Discrete-Velocity Boltzmann Equation

Published online by Cambridge University Press:  03 June 2015

Erlend Magnus Viggen*
Affiliation:
Department of Electronics and Telecommunications, Norwegian University of Science and Technology (NTNU), 7034 Trondheim, Norway
*
*Corresponding author.Email:erlend.vigen ntnu.no
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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.

Type
Research Article
Copyright
Copyright © Global Science Press Limited 2013

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References

[1]Chen, S. and Doolen, G. D., Lattice Boltzmann method for fluid flows, Annu. Rev. Fluid Mech., 30 (1998), 329364.Google Scholar
[2]Dellar, P. J., Bulk and shear viscosities in lattice Boltzmann equations, Phys. Rev. E, 64 (2001), 031203.Google Scholar
[3]Hasert, M., Bernsdorf, J., and Roller, S., Towards aeroacoustic sound generation by flow through porous media, Phil. Trans. R. Soc. A, 369 (2011), 24672475.CrossRefGoogle ScholarPubMed
[4]Wilde, A., Calculation of sound generation and radiation from instationary flows, Comput. Fluids, 35 (2006), 986993.CrossRefGoogle Scholar
[5]Lighthill, M. J., On sound generated aerodynamically I. General theory, Proc. R. Soc. A, 211 (1952), 564587.Google Scholar
[6]Popescu, M., Johansen, S. T., and Shyy, W., Flow-induced acoustics in corrugated pipes, Commun. Comput. Phys., 10 (2011), 120139.Google Scholar
[7]Viggen, E. M., Viscously damped acoustic waves with the lattice Boltzmann method, Phil. Trans. R. Soc. A, 369 (2011), 22462254.Google Scholar
[8]Li, Y. and Shan, X., Lattice Boltzmann method for adiabatic acoustics, Phil. Trans. R. Soc. A, 369 (2011), 23712380.Google Scholar
[9]Blackstock, D. T., Fundamentals of Physical Acoustics, Ch. 9, John Wiley & Sons, 2000.Google Scholar
[10]Truesdell, C., Precise theory of the absorption and dispersion of forced plane infinitesimal waves according to the Navier-Stokes equations, J. Rational Mech. Anal., 2 (1953), 643730.Google Scholar
[11]Latt, J., Hydrodynamic limit of lattice Boltzmann equations, Ch. 2, PhD Thesis, University of Geneva, 2007.Google Scholar
[12]Foch, J. and Uhlenbeck, G. E., Propagation of sound in monatomic gases, Phys. Rev. Lett., 19 (1967), 10251027.Google Scholar
[13]Dellar, P. J., Macroscopic descriptions of rarefied gases from the elimination of fast variables, Phys. Fluids, 19 (2007), 107101.Google Scholar
[14]Greenspan, M., Transmission of sound waves in gases at very low pressures, in Physical Acoustics IIA, Academic Press, 1965.Google Scholar
[15]Wang Chang, C. S. and Uhlenbeck, G. E., The kinetic theory of gases, in Studies in Statistical Mechanics V, North-Holland Publishing Company, 1970.Google Scholar
[16]Foch, J. and Ford, G. W., The dispersion of sound in monatomic gases, in Studies in Statistical Mechanics V, North-Holland Publishing Company, 1970.Google Scholar
[17]Meyer, E. and Sessler, G., Schallausbreitung in Gasen bei hohen Frequenzen und sehr niedrigen Drucken, Z. Phys., 149 (1957), 1539.Google Scholar
[18]Grad, H., On the kinetic theory of rarefied gases, Comm. Pure Appl. Math., 2 (1949), 331407.Google Scholar
[19]Kinsler, L. E., Frey, A. R., Coppens, A. B., and Sanders, J. V., Fundamentals of Acoustics, John Wiley & Sons, 2000.Google Scholar
[20]Bennett, S., A lattice Boltzmann model for diffusion of binary gas mixtures, Ch. 4, PhD Thesis, University of Cambridge, 2010.Google Scholar