The lattice Boltzmann method for turbulent channel flows using graphics processing units

Vanja Zecevic, Michael P. Kirkpatrick, Steven W. Armfield

Abstract


We performed a direct numerical simulation of turbulent channel flow at Reynolds number 180 using the Lattice Boltzmann method. We used the single relaxation time collision operator. The code was executed using graphics processing units as a highly parallel high performance computing platform. Results are compared to published direct numerical simulation results. We avoid common drawbacks of the method, such as compressibility error and instability at higher Reynolds numbers, by using a sufficiently small Mach number and lattice spacing. We validate the Lattice Boltzmann method using the single relaxation time collision operator as an effective tool for continued research into fundamental turbulent flows. The method is less suitable for wall bounded turbulence since these flows benefit from an increased resolution near the wall while the standard Lattice Boltzmann method requires an isotropic, homogeneous lattice. This work validates the method as well as being a guide to suitable parameter ranges and target flows.

References
  • Cyrus K. Aidun and Jonathan R. Clausen. Lattice Boltzmann method for complex flows. Annu. Rev. Fluid Mech., 42:439--472, 2010. doi:10.1146/annurev-fluid-121108-145519
  • P. Bailey, J. Myre, S. D. C. Walsh, D. J. Lilja, and M. O. Saar. Accelerating lattice Boltzmann fluid flow simulations using graphics processors. In International Conference on Parallel Processing, ICPC '09, pages 550--557. Sept 2009. doi:10.1109/ICPP.2009.38
  • R. Benzi, S. Succi, and M. Vergassola. The lattice Boltzmann equation---theory and applications. Phys. Rep., 222(3):145--197, Dec 1992. doi:10.1016/0370-1573(92)90090-M
  • Massimo Bernaschi, Massimiliano Fatica, Simone Melchionna, Sauro Succi, and Efthimios Kaxiras. A flexible high-performance lattice Boltzmann gpu code for the simulations of fluid flows in complex geometries. Concurrency Computat. Pract. Exper., 22(1):1--14, Jan 2010. doi:10.1002/cpe.1466
  • Dustin Bespalko, Andrew Pollard, and Mesbah Uddin. Direct numerical simulation of fully-developed turbulent channel flow using the lattice Boltzmann method and analysis of OpenMP scalability. In High Performance Computing Systems and Applications, volume 5976 of Lect. Notes Comput. Sci., pages 1--19. Springer Berlin, 2010. doi:10.1007/978-3-642-12659-8\protect \global \let \OT1\textunderscore \unhbox \voidb@x \kern .06em\vbox {\hrule width.3em}\OT1\textunderscore 1
  • Z. L. Guo, C. G. Zheng, and B. C. Shi. An extrapolation method for boundary conditions in lattice Boltzmann method. Phys. Fluids, 14(6):2007--2010, Jun 2002. doi:10.1063/1.1471914
  • M. Junk, A. Klar, and L. S. Luo. Asymptotic analysis of the lattice Boltzmann equation. J. Comput. Phys., 210(2):676--704, Dec 10 2005. doi:10.1016/j.jcp.2005.05.003
  • D. Kandhai, A. Koponen, A. Hoekstra, M. Kataja, J. Timonen, and P. M. A. Sloot. Implementation aspects of 3D lattice-bgk: Boundaries, accuracy, and a new fast relaxation method. J. Comput. Phys., 150(2):482--501, Apr 10 1999. doi:10.1006/jcph.1999.6191
  • Waleed Abdel Kareem, Seiichiro Izawa, Ao-Kui Xiong, and Yu Fukunishi. Lattice Boltzmann simulations of homogeneous isotropic turbulence. Comput. Math. Appl., 58(5):1055--1061, Sep 2009. doi:10.1016/j.camwa.2009.02.002
  • Keijo Mattila, Jari Hyvaeluoma, Jussi Timonen, and Tuomo Rossi. Comparison of implementations of the lattice-Boltzmann method. Comput. Math. Appl., 55(7):1514--1524, Apr 2008. doi:10.1016/j.camwa.2007.08.001
  • Keijo Mattila, Jari Hyvaluoma, Tuomo Rossi, Mats Aspnas, and Jan Westerholm. An efficient swap algorithm for the lattice Boltzmann method. Comput. Phys. Commun., 176(3):200--210, Feb 1 2007. doi:10.1016/j.cpc.2006.09.005
  • R. D. Moser, J. Kim, and N. N. Mansour. Direct numerical simulation of turbulent channel flow up to Re$_\tau $=590. Phys. Fluids, 11(4):943--945, Apr 1999. doi:10.1063/1.869966
  • Yan Peng, Wei Liao, Li-Shi Luo, and Lian-Ping Wang. Comparison of the lattice Boltzmann and pseudo-spectral methods for decaying turbulence: Low-order statistics. Comput. Fluids, 39(4):568--591, Apr 2010. doi:10.1016/j.compfluid.2009.10.002
  • J. Toelke and M. Krafczyk. TeraFLOP computing on a desktop pc with gpus for 3D cfd. Int. J. Comput. Fluid Dyn., 22(7):443--456, 2008. doi:10.1080/10618560802238275 4th International Conference for Mesoscopic Methods in Engineering and Science, Munich, Germany, Jul 16--20, 2007.
  • D. A. Wolf-Gladrow. Lattice-gas cellular automata and lattice Boltzmann models---Introduction, volume 1725 of Lect. Notes Math. Springer Berlin, 2000.

Keywords


Lattice Boltzmann; GPU; CUDA; graphics processing unit; DNS; turbulent; channel flow; parallel; HPC

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DOI: http://dx.doi.org/10.21914/anziamj.v52i0.3951



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