Hostname: page-component-8448b6f56d-mp689 Total loading time: 0 Render date: 2024-04-23T17:05:57.709Z Has data issue: false hasContentIssue false
  • English
  • Français

Sound Propagation Properties of the Discrete-Velocity Boltzmann Equation

Published online by Cambridge University Press:  03 June 2015

Erlend Magnus Viggen
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
Get access

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.

Keywords

76Q0576P05Lattice Boltzmann methoddiscrete-velocity Boltzmann equationsound propagationcomputational aeroacoustics
Type
Research Article
Information
Communications in Computational Physics , Volume 13 , Issue 3 , March 2013 , pp. 671 - 684
Copyright
Copyright © Global Science Press Limited 2013

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

[1]Chen, S. and Doolen, G. D., Lattice Boltzmann method for fluid flows, Annu. Rev. Fluid Mech., 30 (1998), 329–364.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), 2467–2475.CrossRefGoogle ScholarPubMed
[4]Wilde, A., Calculation of sound generation and radiation from instationary flows, Comput. Fluids, 35 (2006), 986–993.CrossRefGoogle Scholar
[5]Lighthill, M. J., On sound generated aerodynamically I. General theory, Proc. R. Soc. A, 211 (1952), 564–587.Google Scholar
[6]Popescu, M., Johansen, S. T., and Shyy, W., Flow-induced acoustics in corrugated pipes, Commun. Comput. Phys., 10 (2011), 120–139.Google Scholar
[7]Viggen, E. M., Viscously damped acoustic waves with the lattice Boltzmann method, Phil. Trans. R. Soc. A, 369 (2011), 2246–2254.Google Scholar
[8]Li, Y. and Shan, X., Lattice Boltzmann method for adiabatic acoustics, Phil. Trans. R. Soc. A, 369 (2011), 2371–2380.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), 643–730.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), 1025–1027.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), 15–39.Google Scholar
[18]Grad, H., On the kinetic theory of rarefied gases, Comm. Pure Appl. Math., 2 (1949), 331–407.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