Abstract
The lattice Boltzmann method (LBM) is coupled with the multiple-relaxation-time (MRT) collision model and the three-dimensional 19-discrete-velocity (D3Q19) model to resolve intermittent behaviors on small scales in isotropic turbulent flows. The high-order scaling exponents of the velocity structure functions, the probability distribution functions of Lagrangian accelerations, and the local energy dissipation rates are investigated. The self-similarity of the space-time velocity structure functions is explored using the extended self-similarity (ESS) method, which was originally developed for velocity spatial structure functions. The scaling exponents of spatial structure functions at up to ten orders are consistent with the experimental measurements and theoretical results, implying that the LBM can accurately resolve the intermittent behaviors. This validation provides a solid basis for using the LBM to study more complex processes that are sensitive to small scales in turbulent flows, such as the relative dispersion of pollutants and mesoscale structures of preferential concentration of heavy particles suspended in turbulent flows.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
Falkovich, G., Fouxon, A., and Stepanov, M. G. Acceleration of rain initiation by cloud turbulence. nature, 419, 151–154 (2002)
Dimotakis, P. E. Turbulent mixing. Annual Review of Fluid Mechanics, 37, 329–356 (2005)
Wang, L. P., Wexler, A. S., and Zhou, Y. Statistical mechanical description and modelling of turbulent collision of inertial particles. Journal of Fluid Mechanics, 415, 117–153 (2000)
Moin, P. and Mahesh, K. Direct numerical simulation: a tool in turbulence research. Annual Review of Fluid Mechanics, 30, 539–578 (1998)
Wang, L. M., Zhou, G. F., Wang, X. W., Xiong, Q. G., and Ge, W. Direct numerical simulation of particle-fluid systems by combining time-driven hard-sphere model and lattice Boltzmann method. Particuology, 8(4), 379–382 (2010)
Qian, Y. H., Dhumieres, D., and Lallemand, P. Lattice BGK models for Navier-Stokes equation. Europhysics Letters, 17, 479–484 (1992)
Chen, H. D., Chen, S. Y., and Matthaeus, W. H. A Recovery of the Navier-Stokes equations using a lattice-gas Boltzmann method. Physical Review A, 45(8), R5339–R5342 (1992)
Lallemand, P. and Luo, L. S. Theory of the lattice Boltzmann method: dispersion, dissipation, isotropy, Galilean invariance, and stability. Physical Review E, 61(6), 6546–6562 (2000)
Chen, S. Y., Wang, Z., Shan, X. W., and Doolen, G. D. A Lattice Boltzmann computational fluid- dynamics in three dimensions. Journal of Statistical Physics, 68(3/4), 379–400 (1992)
Peng, Y., Liao, W., Luo, L. S., and Wang, L. P. Comparison of the lattice Boltzmann and pseudo- spectral methods for decaying turbulence: low-order statistics. Computers and Fluids, 39(4), 568–591 (2010)
Eggels, J. G. M. Direct and large-eddy simulation of turbulent fluid flow using the lattice- Boltzmann scheme. International Journal of Heat and Fluid Flow, 17(3), 307–323 (1996)
Kim, J., Moin, P., and Moser, R. Turbulence statistics in fully-developed channel flow at low Reynolds-number. Journal of Fluid Mechanics, 177, 133–166 (1987)
Dorschner, B., Bosch, F., Chikatamarla, S. S., Boulouchos, K., and Karlin, I. V. Entropic multi- relaxation time lattice Boltzmann model for complex flows. Journal of Fluid Mechanics, 801, 623–651 (2016)
Wang, P., Wang, L. P., and Guo, Z. L. Comparison of the lattice Boltzmann equation and discrete unified gas-kinetic scheme methods for direct numerical simulation of decaying turbulent flows. Physical Review E, 94(4), 043304 (2016)
D’Humi`eres, D., Ginzburg, I., Krafczyk, M., Lallemand, P., and Luo, L. S. Multiple-relaxation- time lattice Boltzmann models in three dimensions. Philosophical Transactions of the Royal Society of London Series A-Mathematical Physical and Engineering Sciences, 360, 437–451 (2002)
Alvelius, K. Random forcing of three-dimensional homogeneous turbulence. Physics of Fluids, 11(7), 1880–1889 (1999)
Cate, A. T., Derksen, J. J., Portela, L. M., and van den Akker, H. E. A. Fully resolved simulations of colliding monodisperse spheres in forced isotropic turbulence. Journal of Fluid Mechanics, 519, 233–271 (2004)
Benzi, R., Ciliberto, S., Tripiccione, R., Baudet, C., Massaioli, F., and Succi, S. Extended self- similarity in turbulent flows. Physical Review E, 48(1), 29–32 (1993)
Pope, S. B. Turbulent Flows, Cambridge University Press, Cambridge (2000)
Anselmet, F., Gagne, Y., Hopfinger, E. J., and Antonia, R. A. High-order velocity structure functions in turbulent shear flows. Journal of Fluid Mechanics, 140, 63–89 (1984)
Vincent, A. and Meneguzzi, M. The spatial structure and statistical properties of homogeneous turbulence. Journal of Fluid Mechanics, 225, 1–20 (1991)
She, Z. S. and Leveque, E. Universal scaling laws in fully-developed turbulence. Physical Review Letters, 72(3), 336–339 (1994)
Arneodo, A., Baudet, C., Belin, F., Benzi, R., Castaing, B., Chabaud, B., Chavarria, R., Ciliberto, S., Camussi, R., Chill`a, F., Dubrulle, B., Gagne, Y., Hebral, B., Herweijer, J., Marchand, M., Maurer, J., Muzy, Z. F., Naert, A., Noullez, A., Peinke, J., Tabeling, P., van der Water, W., and Willaime, H. Structure functions in turbulence, in various flow configurations, at Reynolds number between 30 and 5 000, using extended self-similarity. Europhysics Letters, 34(6), 411–416 (1996)
De Silva, C. M., Marusic, I., Woodcock, J. D., and Meneveau, C. Scaling of second- and higher- order structure functions in turbulent boundary layers. Journal of Fluid Mechanics, 769, 654–686 (2015)
Toschi, F., Amati, G., Succi, S., Benzi, R., and Piva, R. Intermittency and structure functions in channel flow turbulence. Physical Review Letters, 82(25), 5044–5047 (1999)
Wang, L. P., Min, H. D., Peng, C., Geneva, N., and Guo, Z. L. A lattice-Boltzmann scheme of the Navier-Stokes equation on a three-dimensional cuboid lattice. Computers and Mathematics with Applications, 2016 (2016) https://doi.org/10.1016/j.camwa.2016.06.017
Amati, G., Succi, S., and Piva, R. Massively parallel lattice-Boltzmann simulation of turbulent channel flow. International Journal of Modern Physics C, 8, 869–877 (1996)
Voth, G. A., La Porta, A., Crawford, A. M., Alexander, J., and Bodenschatz, E. Measurement of particle accelerations in fully developed turbulence. Journal of Fluid Mechanics, 469, 121–160 (2002)
Mordant, N., Crawford, A.M., and Bodenschatz, E. Three-dimensional structure of the Lagrangian acceleration in turbulent flows. Physical Review Letters, 93(21), 214501 (2004)
Mordant, N., Leveque, E., and Pinton, J. F. Experimental and numerical study of the Lagrangian dynamics of high Reynolds turbulence. New Journal of Physics, 6(116), 1–44 (2004)
Bec, J., Biferale, L., Boffetta, G., Celani, A., Cencini, M., Lanotte, A., Musacchio, S., and Toschi, F. Acceleration statistics of heavy particles in turbulence. Journal of Fluid Mechanics, 550, 349–358 (2006)
Biferale, L., Boffetta, G., Celani, A., Devenish, B. J., Lanotte, A., and Toschi, F. Multifractal statistics of Lagrangian velocity and acceleration in turbulence. Physical Review Letters, 93(6), 064502 (2004)
Acknowledgements
Simulations were run on the super-computer of Tianhe-1A at the National Supercomputer Center in Tianjin, China.
Author information
Authors and Affiliations
Corresponding author
Additional information
Citation: Jin, G. D., Wang, S. Z., Wang, Y., and He, G. W. Lattice Boltzmann simulations of high-order statistics in isotropic turbulent flows. Applied Mathematics and Mechanics (English Edition), 39(1), 21–30 (2018) https://doi.org/10.1007/s10483-018-2254-9
Project supported by the Science Challenge Program (No. TZ2016001), the National Natural Science Foundation of China (Nos. 11472277, 11572331, 11232011, and 11772337), the Strategic Priority Research Program, Chinese Academy of Sciences (CAS) (No. XDB22040104), the Key Research Program of Frontier Sciences, CAS (No. QYZDJ-SSW-SYS002), and the National Basic Research Program of China (973 Program) (No. 2013CB834100)
Rights and permissions
About this article
Cite this article
Jin, G., Wang, S., Wang, Y. et al. Lattice Boltzmann simulations of high-order statistics in isotropic turbulent flows. Appl. Math. Mech.-Engl. Ed. 39, 21–30 (2018). https://doi.org/10.1007/s10483-018-2254-9
Received:
Revised:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10483-018-2254-9
Key words
- mesoscopic modelling
- lattice Boltzmann method (LBM)
- isotropic turbulent flow
- structure function
- intermittency
- high-order statistics
- self-similarity