Skip to main content Accessibility help

Aeroacoustic Simulations Using Compressible Lattice Boltzmann Method

  • Kai Li (a1) and Chengwen Zhong (a1)


This paper presents a lattice Boltzmann (LB) method based study aimed at numerical simulation of aeroacoustic phenomenon in flows around a symmetric obstacle. To simulate the compressible flow accurately, a potential energy double-distribution-function (DDF) lattice Boltzmann method is used over the entire computational domain from the near to far fields. The buffer zone and absorbing boundary condition is employed to eliminate the non-physical reflecting. Through the direct numerical simulation, the flow around a circular cylinder at Re=150, M=0.2 and the flow around a NACA0012 airfoil at Re=10000, M=0.8, α=0° are investigated. The generation and propagation of the sound produced by the vortex shedding are reappeared clearly. The obtained results increase our understanding of the characteristic features of the aeroacoustic sound.


Corresponding author

*Corresponding author. (K. Li), (C.W. Zhong)


Hide All
[1]Li, X., Leung, R. K. and So, R. C., One-step aeroacoustics simulation using lattice Boltzmann method, AIAA J., 44 (2006), pp. 7889.
[2]Viggen, E. M., Viscously damped acoustic waves with the lattice Boltzmann method, Philos. T. Roy. Soc. A, 369 (2011), pp. 22462254.
[3]Tajiri, S., Tsutahara, M. and Tanaka, H., Direct simulation of sound and underwater sound generated by a water drop hitting a water surface using the finite difference lattice Boltzmann method, Comput. Math. Appl., 59 (2010), pp. 24112420.
[4]Ikeda, T., Atobe, T. and Takagi, S., Direct simulations of trailing-edge noise generation from two-dimensional airfoils at low Reynolds numbers, J. Sound Vibration, 331 (2012), pp. 556574.
[5]Kusano, K., Yamada, K. and Furukawa, M., Toward direct numerical simulation of aeroacoustic field around airfoil using multi-scale lattice Boltzmann method, ASME 2013 Fluids Engineering Division Summer Meeting, American Society of Mechanical Engineers, Nevada, USA, 2013, V01AT09A005.
[6]Xu, A., Zhang, G., Li, Y. and Li, H., Modeling and simulation of nonequilibrium and multiphase complex systems: lattice Boltzmann kinetic theory and application, Progress Phys., 34 (2014), pp. 136167, in Chinese.
[7]Xu, A., Lin, C., Zhang, G. and Li, Y., Multiple-relaxation-time lattice Boltzmann kinetic model for combustion, Phys. Rev. E, 91 (2015), 043306.
[8]Bhatnagar, P. L., Gross, E. P. and Krook, M., A model for collision processes in gases i. small amplitude processes in charged and neutral one-component systems, Phys. Rev., 94 (1954), pp. 511525.
[9]Succi, S., The Lattice Boltzmann Equation: for Fluid Dynamics and Beyond, Oxford University Press, 2001.
[10]Xu, A. G., Zhang, G. C., Gan, Y. B., Chen, F. and Yu, X. J., Lattice Boltzmann modeling and simulation of compressible flows, Frontiers Phys., 7 (2012), pp. 582600.
[11]Alexander, F. J., Chen, S. and Sterling, J. D., Lattice Boltzmann thermohydrodynamics, Phys. Rev. E, 47 (1993), pp. R2249–R2252.
[12]Qian, Y., Simulating thermohydrodynamics with lattice BGK models, J. Sci. Comput., 8 (1993), pp. 231242.
[13]Yan, G., Chen, Y. and Hu, S., Simple lattice Boltzmann model for simulating flows with shock wave, Phys. Rev. E, 59 (1999), pp. 454459.
[14]Yan, G., Zhang, J., Liu, Y. and Dong, Y., A multi-energy-level lattice Boltzmann model for the compressible Navier-Stokes equations, Int. J. Numer. Methods Fluids, 55 (2007), pp. 4156.
[15]Sun, C., Lattice-Boltzmann models for high speed flows, Phys. Rev. E, 58 (1998), pp. 72837287.
[16]Sun, C., Adaptive lattice Boltzmann model for compressible flows: viscous and conductive properties, Phys. Rev. E, 61 (2000), pp. 26452653.
[17]Shi, W., Shyy, W. and Mei, R., Finite-difference-based lattice Boltzmann method for inviscid compressible flows, Numer. Heat Transfer B Fundamentals, 40 (2001), pp. 121.
[18]Kataoka, T. and Tsutahara, M., Lattice Boltzmann model for the compressible Euler equations, Phys. Rev. E, 69 (2004), 056702.
[19]Kataoka, T. and Tsutahara, M., Lattice Boltzmann model for the compressible Navier-Stokes equations with flexible specific-heat ratio, Phys. Rev. E, 69 (2004), 035701.
[20]Watari, M., Finite difference lattice Boltzmann method with arbitrary specific heat ratio applicable to supersonic flow simulations, Phys. A Stat. Mech. Appl., 382 (2007), pp. 502522.
[21]He, X., Chen, S. and Doolen, G. D., A novel thermal model for the lattice Boltzmann method in incompressible limit, J. Comput. Phys., 146 (1998), pp. 282300.
[22]Guo, Z., Zheng, C., Shi, B. and Zhao, T. S., Thermal lattice Boltzmann equation for low Mach number flows: decoupling model, Phys. Rev. E, 75 (2007), 036704.
[23]Li, K. and Zhong, C., A lattice Boltzmann model for simulation of compressible flows, Int. J. Numer. Methods Fluids, 77 (2015), pp. 334357.
[24]Buick, J., Greated, C. and Campbell, D., Lattice BGK simulation of sound waves, Europhys. Lett., 43 (1998), pp. 235240.
[25]Buick, J., Buckley, C., Greated, C. and Gilbert, J., Lattice Boltzmann BGK simulation of nonlinear sound waves: the development of a shock front, J. Phys. A Math. General, 33 (2000), pp. 39173928.
[26]Haydock, D. and Yeomans, J., Lattice Boltzmann simulations of acoustic streaming, J. Phys. A Math. General, 34 (2001), pp. 52015213.
[27]Marié, S., Ricot, D. and Sagaut, P., Accuracy of lattice Boltzmann method for aeroacoustics simulations, AIAA Paper, 3515 (2007).
[28]Marié, S., Ricot, D. and Sagaut, P., Comparison between lattice Boltzmann method and Navier-Stokes high order schemes for computational aeroacoustics, J. Comput. Phys., 228 (2009), pp. 10561070.
[29]Xu, H. and Sagaut, P., Optimal low-dispersion low-dissipation LBM schemes for computational aeroacoustics, J. Comput. Phys., 230 (2011), pp. 53535382.
[30]Kang, H. K., Ro, K. D., Tsutahara, M. and Lee, Y. H., Numerical prediction of acoustic sounds occurring by the flow around a circular cylinder, KSME Int. J., 17 (2003), pp. 12191225.
[31]Tsutahara, M., Kondo, T. and Mochizuki, K., Direct simulations of acoustic waves by finite volume lattice Boltzmann method, AIAA Paper, 2570 (2006).
[32]Laffite, A. and Pérot, F., Investigation of the noise generated by cylinder flows using a direct lattice-Boltzmann approach, AIAA Paper, 3268 (2009).
[33]Tamura, A., Tsutahara, M., Kataoka, T., Aoyama, T. and Yang, C., Numerical simulation of two-dimensional blade-vortex interactions using the finite difference lattice Boltzmann method, AIAA J., 46 (2008), pp. 22352247.
[34]Satti, R., Lew, P. T., Li, Y., Shock, R. and Noelting, S., Unsteady flow computations and noise predictions on a rod-airfoil using lattice Boltzmann method, AIAA Paper, 497 (2009).
[35]Jones, L. E., Numerical Studies of the Flow Around an Airfoil at Low Reynolds Number, PhD thesis, University of Southampton, 2008.
[36]Qu, K., Development of Lattice Boltzmann Method for Compressible Flows, PhD thesis, National University of Singapore, 2009.
[37]Li, Q., He, Y. L., Wang, Y. and Tao, W. Q., Coupled double-distribution-function lattice Boltzmann method for the compressible Navier-Stokes equations, Phys. Rev. E, 76 (2007), 056705.
[38]Tsutahara, M., The finite-difference lattice Boltzmann method and its application in computational aero-acoustics, Fluid Dyn. Research, 44 (2012), 045507.
[39]Van Leer, B., Towards the ultimate conservative difference scheme. v. a second-order sequel to godunov's method, J. Comput. Phys., 32 (1979), pp. 101136.
[40]Kermani, M., Gerber, A. and Stockie, J., Thermodynamically based moisture prediction using Roe's scheme, 4th Conference of Iranian Aerospace Society, Amir Kabir University of Technology, Tehran, Iran, 2003, pp. 2729.
[41]Pareschi, L. and Russo, G., Implicit-explicit Runge-Kutta schemes and applications to hyperbolic systems with relaxation, J. Sci. Comput., 25 (2005), pp. 129155.
[42]Patil, D., Chapman-Enskog analysis for finite-volume formulation of lattice Boltzmann equation, Phys. A Stat. Mech. Appl., 392 (2013), pp. 27012712.
[43]Van Albada, G., Van Leer, B. and Roberts, W. Jr, A comparative study of computational methods in cosmic gas dynamics, Astronomy Astrophys., 108 (1982), pp. 7684.
[44]Guo, Z., Zheng, C. and Shi, B., Non-equilibrium extrapolation method for velocity and pressure boundary conditions in the lattice Boltzmann method, Chinese Phys., 11 (2002), pp. 366374.
[45]Da Silva, A. R., Numerical Studies of Aeroacoustic Aspects of Wind Instruments, PhD thesis, McGill University, 2008.
[46]Inoue, O. and Hatakeyama, N., Sound generation by a two-dimensional circular cylinder in a uniform flow, J. Fluid Mech., 471 (2002), pp. 285314.
[47]Tsutahara, M., Kataoka, T., Shikata, K. and Takada, N., New model and scheme for compressible fluids of the finite difference lattice Boltzmann method and direct simulations of aerodynamic sound, Comput. Fluids, 37 (2008), pp. 7989.
[48]Mavriplis, D. J. and Jameson, A., Multigrid solution of the Navier-Stokes equations on triangular meshes, AIAA J., 28 (1990), pp. 14151425.
[49]Bassi, F. and Rebay, S., A high-order accurate discontinuous finite element method for the numerical solution of the compressible Navier-Stokes equations, J. Comput. Phys., 131 (1997), pp. 267279.
[50]Bouhadji, A. and Braza, M., Organised modes and shock-vortex interaction in unsteady viscous transonic flows around an aerofoil: part i: Mach number effect, Comput. Fluids, 32 (2003), pp. 12331260.


MSC classification

Related content

Powered by UNSILO

Aeroacoustic Simulations Using Compressible Lattice Boltzmann Method

  • Kai Li (a1) and Chengwen Zhong (a1)


Full text views

Total number of HTML views: 0
Total number of PDF views: 0 *
Loading metrics...

Abstract views

Total abstract views: 0 *
Loading metrics...

* Views captured on Cambridge Core between <date>. This data will be updated every 24 hours.

Usage data cannot currently be displayed.