Volume 13, Issue 3
Sound Propagation Properties of the Discrete-Velocity Boltzmann Equation

Erlend Magnus Viggen

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

Published online: 2013-03

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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 foundforthisequation. ThisexpressioniscomparedtosimilaronesfromtheNavierStokes 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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@Article{CiCP-13-671, author = {Erlend Magnus Viggen}, title = {Sound Propagation Properties of the Discrete-Velocity Boltzmann Equation}, journal = {Communications in Computational Physics}, year = {2013}, volume = {13}, number = {3}, pages = {671--684}, 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 foundforthisequation. ThisexpressioniscomparedtosimilaronesfromtheNavierStokes 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.


}, issn = {1991-7120}, doi = {https://doi.org/10.4208/cicp.271011.020212s}, url = {http://global-sci.org/intro/article_detail/cicp/7242.html} }
TY - JOUR T1 - Sound Propagation Properties of the Discrete-Velocity Boltzmann Equation AU - Erlend Magnus Viggen JO - Communications in Computational Physics VL - 3 SP - 671 EP - 684 PY - 2013 DA - 2013/03 SN - 13 DO - http://dor.org/10.4208/cicp.271011.020212s UR - https://global-sci.org/intro/cicp/7242.html KW - AB -

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 foundforthisequation. ThisexpressioniscomparedtosimilaronesfromtheNavierStokes 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.


Erlend Magnus Viggen. (1970). Sound Propagation Properties of the Discrete-Velocity Boltzmann Equation. Communications in Computational Physics. 13 (3). 671-684. doi:10.4208/cicp.271011.020212s
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