Skip to main content Accessibility help
×
Home

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
E-mail address:
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.

Type
Research Article
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.

References

[1]Chen, S. and Doolen, G. D., Lattice Boltzmann method for fluid flows, Annu. Rev. Fluid Mech., 30 (1998), 329364.CrossRefGoogle Scholar
[2]Dellar, P. J., Bulk and shear viscosities in lattice Boltzmann equations, Phys. Rev. E, 64 (2001), 031203.CrossRefGoogle ScholarPubMed
[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.CrossRefGoogle Scholar
[6]Popescu, M., Johansen, S. T., and Shyy, W., Flow-induced acoustics in corrugated pipes, Commun. Comput. Phys., 10 (2011), 120139.CrossRefGoogle Scholar
[7]Viggen, E. M., Viscously damped acoustic waves with the lattice Boltzmann method, Phil. Trans. R. Soc. A, 369 (2011), 22462254.CrossRefGoogle ScholarPubMed
[8]Li, Y. and Shan, X., Lattice Boltzmann method for adiabatic acoustics, Phil. Trans. R. Soc. A, 369 (2011), 23712380.CrossRefGoogle ScholarPubMed
[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.CrossRefGoogle Scholar
[13]Dellar, P. J., Macroscopic descriptions of rarefied gases from the elimination of fast variables, Phys. Fluids, 19 (2007), 107101.CrossRefGoogle Scholar
[14]Greenspan, M., Transmission of sound waves in gases at very low pressures, in Physical Acoustics IIA, Academic Press, 1965.CrossRefGoogle 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.CrossRefGoogle Scholar
[18]Grad, H., On the kinetic theory of rarefied gases, Comm. Pure Appl. Math., 2 (1949), 331407.CrossRefGoogle 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

Full text views

Full text views reflects PDF downloads, PDFs sent to Google Drive, Dropbox and Kindle and HTML full text views.

Total number of HTML views: 0
Total number of PDF views: 23 *
View data table for this chart

* Views captured on Cambridge Core between September 2016 - 25th January 2021. This data will be updated every 24 hours.

Hostname: page-component-76cb886bbf-86jzp Total loading time: 0.25 Render date: 2021-01-25T05:42:41.171Z Query parameters: { "hasAccess": "0", "openAccess": "0", "isLogged": "0", "lang": "en" } Feature Flags: { "shouldUseShareProductTool": true, "shouldUseHypothesis": true, "isUnsiloEnabled": true, "metricsAbstractViews": false, "figures": false, "newCiteModal": false }

Send article to Kindle

To send this article to your Kindle, first ensure no-reply@cambridge.org is added to your Approved Personal Document E-mail List under your Personal Document Settings on the Manage Your Content and Devices page of your Amazon account. Then enter the ‘name’ part of your Kindle email address below. Find out more about sending to your Kindle. Find out more about sending to your Kindle.

Note you can select to send to either the @free.kindle.com or @kindle.com variations. ‘@free.kindle.com’ emails are free but can only be sent to your device when it is connected to wi-fi. ‘@kindle.com’ emails can be delivered even when you are not connected to wi-fi, but note that service fees apply.

Find out more about the Kindle Personal Document Service.

Sound Propagation Properties of the Discrete-Velocity Boltzmann Equation
Available formats
×

Send article to Dropbox

To send this article to your Dropbox account, please select one or more formats and confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your <service> account. Find out more about sending content to Dropbox.

Sound Propagation Properties of the Discrete-Velocity Boltzmann Equation
Available formats
×

Send article to Google Drive

To send this article to your Google Drive account, please select one or more formats and confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your <service> account. Find out more about sending content to Google Drive.

Sound Propagation Properties of the Discrete-Velocity Boltzmann Equation
Available formats
×
×

Reply to: Submit a response


Your details


Conflicting interests

Do you have any conflicting interests? *