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, 76P05Notice: Undefined variable: pac in /var/www/html/issue/abstract/readabs.php on line 164 Key words: Lattice Boltzmann method, discrete-velocity Boltzmann equation, sound propagation, computational aeroacoustics. *Corresponding author. Email: erlend.viggen@ntnu.no (E. M. Viggen) |