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Large Eddy Simulation-Based Lattice Boltzmann Method with Different Collision Models

  • Mohamed Hamdi
  • Souheil Elalimi
  • Sassi Ben Nasrallah
Chapter
Part of the Green Energy and Technology book series (GREEN)

Abstract

It is of interest to discuss the analogies between ELB and LBM with turbulence models. This paper addresses the issue of incorporation of the subgrid turbulence model in the lattice Boltzmann equation (LBE). A lattice Boltzmann solver is implemented using various techniques, and the performance will be discussed. The numerical validity of the codes is tested against known fluid flow solutions, and a visual representation of the fluid flow is created. The simulations include lattice Boltzmann method with subgrid model and single-relaxation-time (SRT), multiple-relaxation-time (MRT), and entropic collision models (ELBM). We explore the behavior and accuracy of the proposed models on lid-driven square cavity at Reynolds number up to 10.000. Our results clearly show that the LES-MRT model remains the most effective in terms of accuracy and stability. Also our results highlight the subgrid features of the ELBE.

Keywords

LBE SRT MRT ELB Subgrid Accuracy Stability 

References

  1. Ansumali, S., Karlin, I.: Kinetic boundary conditions in the lattice Boltzmann method. Phys. Rev. E. 66(2), 026311 (2002)MathSciNetCrossRefGoogle Scholar
  2. Ansumali, S., Karlin, I.V., Öttinger, H.C.: Minimal entropic kinetic models for hydrodynamics. Europhys. Lett. 63, 798–804 (2003)CrossRefGoogle Scholar
  3. Arcidiacono, S., Karlin, I.V., Mantzaras, J., Frouzakis, C.E.: Lattice Boltzmann model for the simulation of multicomponent mixtures. Phys. Rev. E. 76, 046703 (2007)CrossRefGoogle Scholar
  4. Bhatnagar, P.L., Gross, E.P., Krook, M.: A model for collision processes in gases. I. Small amplitude processes in charged and neutral one-component systems. Phys. Rev. 94, 511 (1954)CrossRefGoogle Scholar
  5. Chen, S.: A large-eddy-based lattice Boltzmann model for turbulent flow simulation. Appl. Math. Comput. 215(2), 591–598 (2009)Google Scholar
  6. Chikatamarla, S., Karlin, I.: Lattices for lattice Boltzmann method. Phys. Rev. E. 79, 046701 (2009)MathSciNetCrossRefGoogle Scholar
  7. Chikatamarla, S.S., Ansumali, S., Karlin, I.V.: Grad’s approximation for missing data in lattice Boltzmann simulations. Europhys. Lett. 74(2), 215–221 (2006)MathSciNetCrossRefGoogle Scholar
  8. D’Humieres, D., Irina, G., Manfred, K., Pierre, L., Luo, L.-S.: Multiple-relaxation-time lattice Boltzmann models in three dimensions. Phil. Trans. R. Soc. Lond. Series A-Math. Phys. Eng. Sci. 360(1792), 437–451 (2002)MathSciNetCrossRefGoogle Scholar
  9. Deng, L., Zhang, Y., Wen, Y., Zhou, H.: A fractional-step thermal lattice Boltzmann model for high Peclet number flow. Comput. Math. Appl. 70(5), 1152–1161 (2015)Google Scholar
  10. Ding, Y., Kawahara, M.: Linear stability of incompressible fluid flow in a cavity using finite element method. Int. J. Numer. Methods Fluids. 27, 139–157 (1998)MathSciNetCrossRefGoogle Scholar
  11. Dong, Y.-H., Sagaut, P., Marie, S.: Inertial consistent subgrid model for large-eddy simulation based on the lattice Boltzmann method. Phys. Fluids. 20, 035104 (2008)CrossRefGoogle Scholar
  12. Dubois, F., Lallemand, P., Tekitek, M.: On a superconvergent lattice Boltzmann boundary scheme. Comput. Math. Appl. 59(7), 2141–2149 (2010)MathSciNetCrossRefGoogle Scholar
  13. Eggels, J.G.M.: Direct and large-eddy simulation of turbulent fluid flow using the lattice-Boltzmann scheme. Int. J. Heat Fluid Flow. 17(3), 307–323 (1996)CrossRefGoogle Scholar
  14. Erturk, E.: Discussions on driven cavity flow. Int. J. Numer. Meth. Fluids. 60, 275–294 (2009)MathSciNetCrossRefGoogle Scholar
  15. Erturk, E., Corke, T.C., Gokcol, C.: Numerical solutions of 2-D steady incompressible driven cavity flow at high Reynolds numbers. Int. J. Numer. Methods Fluids. 48, 747–774 (2005)CrossRefGoogle Scholar
  16. Ghia, U., Ghia, K.N., Shin, C.T.: High-re solutions for incompressible flow using the Navier-Stokes equations and a multigrid method. J. Comput. Phys. 48, 387–411 (1982)CrossRefGoogle Scholar
  17. Ginzburg, I.: Equilibrium-type and link-type lattice Boltzmann models for generic advection and anisotropic-dispersion equation. Adv. Water Resour. 28(11), 1171–1195 (2005)CrossRefGoogle Scholar
  18. Ginzburg, I., Alder, P.M.: Boundary flow condition analysis for the three-dimensional lattice Boltzmann model. J. Phys. II. 4, 191–214 (1994)Google Scholar
  19. Ginzburg, I., d’Humières, D.: Multireflection boundary conditions for lattice Boltzmann models. Phys. Rev. E. 68, 066614 (2002)MathSciNetCrossRefGoogle Scholar
  20. Ginzburg, I., Verhaeghe, F., d’Humieres, D.: Two-relaxation-time lattice Boltzmann scheme: about parametrization, velocity, pressure and mixed boundary conditions. Commun. Comput. Phys. 3(2), 427–478 (2008)MathSciNetGoogle Scholar
  21. Hachem, E., Rivaux, B., Kloczko, T., Digonnet, H., Coupez, T.: Stabilized finite element method for incompressible flows with high Reynolds number. J. Comput. Phys. 229, 8643–8665 (2010)MathSciNetCrossRefGoogle Scholar
  22. He, X., Luo, L.-S.: Theory of the lattice Boltzmann method: from the Boltzmann equation to the lattice Boltzmann equation. Phys. Rev. E. 56, 6811 (1997)CrossRefGoogle Scholar
  23. Hou, S., Sterling, J., Chen, S., Doolen, G.D.: A lattice Boltzmann Subgrid model for high Reynolds number flows. Fields Inst. Comm. 6, 151–166 (1996)MathSciNetzbMATHGoogle Scholar
  24. Karlin, I.V., Succi, S., Chikatamarla, S.S.: Comment on “Numerics of the lattice Boltzmann method: effects of collision models on the lattice Boltzmann simulations”. Phys. Rev. E Stat. Nonlinear Soft Matter Phys. 84, 068701 (2011a)CrossRefGoogle Scholar
  25. Karlin, I., Asinari, P., Succi, S.: Matrix lattice Boltzmann reloaded. Phil. Trans. R. Soc. A. 369, 2202–2210 (2011b)MathSciNetCrossRefGoogle Scholar
  26. Keating, B., Vahala, G.: Entropic lattice Boltzmann representations required to recover Navier-Stokes flows. Phys. Rev. E. 75, 036712 (2007)MathSciNetCrossRefGoogle Scholar
  27. Krafczyk, M., Tölke, J., Luo, L.S.: Large-eddy simulations with a multiple-relaxation-time LBE model. Int. J. Mod. Phys. B. 17, 33–39 (2003)CrossRefGoogle Scholar
  28. Lachowicz, M.: Links between microscopic and macroscopic descriptions. Multiscale Prob. Life Sci., Lecture Notes in Mathematics. 1940, 201–267 (2008)Google Scholar
  29. Lallemand, P., Luo, L.-S.: Theory of the lattice Boltzmann method: dispersion, dissipation, isotropy, Galilean invariance, and stability. Phys. Rev. E. 61, 6546 (2000)MathSciNetCrossRefGoogle Scholar
  30. Lu, Z., Liao, Y., Qian, D., McLaughlin, J.B., Derksen, J.J., Kontomaris, K.: Large eddy simulations of a stirred tank using the lattice Boltzmann method on a Nonuniform grid. J. Comput. Phys. 181, 675–704 (2002)CrossRefGoogle Scholar
  31. Luo, L.S., Liao, W., Chen, X., Peng, Y., Zhang, W.: Numerics of the lattice Boltzmann method: effects of collision models on the lattice Boltzmann simulations. Phys. Rev. E. 83(056710), 1–24 (2011)Google Scholar
  32. Malaspinas, O., Deville, M., Chopard, B.: Towards a physical interpretation of the entropic lattice Boltzmann method. Phys. Rev. E. 78, 066705 (2008)Google Scholar
  33. Malaspinas, O., Sagaut, P.: Advanced large-eddy simulation for lattice Boltzmann methods: the approximate deconvolution model. Phys. Fluids. 23, 105103 (2011)CrossRefGoogle Scholar
  34. Mohamad, A.A.: Applied Lattice Boltzmann Method for Transport Phenomena, Momentum, Heat and Mass Transfer. Sure Print, Calgary (2007)Google Scholar
  35. Rogallo, R.S., Moin, P.: Numerical simulation of turbulent flows. Ann. Rev. 16, 99–137 (1984)zbMATHGoogle Scholar
  36. Sagaut, P.: Toward advanced subgrid models for lattice-Boltzmann-based large-eddy simulation: theoretical formulations. Comput. Math. Appl. 59(7), 2194–2199 (2010)MathSciNetCrossRefGoogle Scholar
  37. Sauro, S.: The Lattice Boltzmann Equation for Fluid Dynamics and Beyond (Numerical Mathematics and Scientific Computation). Clarendon Press, Oxford (2001)zbMATHGoogle Scholar
  38. Schlatter, P., Stolz, S., Kleiser, L.: Large-eddy simulation of spatial transition in plane channel flow. J. Turbul. 7, 1–24 (2006)MathSciNetCrossRefGoogle Scholar
  39. Shua, C., Niua, X.D., Chewa, Y.T., Caib, Q.D.: A fractional step lattice Boltzmann method for simulating high Reynolds number flows. Math. Comput. Simul. 72, 201–205 (2006)MathSciNetCrossRefGoogle Scholar
  40. Stolz, S., Adams, N.A.: An approximate deconvolution procedure for large-eddy simulation. Phys. Fluids. 11(7), 1699–1701 (1999)CrossRefGoogle Scholar
  41. Wang, J., Wang, D., Lallemand, P., Luo, L.-S.: Lattice Boltzmann simulations of thermal convective flows in two dimensions. Comput. Math. Appl. 65, 262–286 (2013)MathSciNetCrossRefGoogle Scholar
  42. Weickert, M., Teike, G., Schmidt, O., Sommerfeld, M.: Investigation of the LES WALE turbulence model within the lattice Boltzmann framework. Comput. Math. Appl. 59(7), 2200–2214 (2010)MathSciNetCrossRefGoogle Scholar
  43. Yasuda, T., Satofuka, N.: An improved entropic lattice Boltzmann model for parallel computation. Comput. Fluids. 45(1), 187–190 (2011)MathSciNetCrossRefGoogle Scholar

Copyright information

© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  • Mohamed Hamdi
    • 1
  • Souheil Elalimi
    • 2
  • Sassi Ben Nasrallah
    • 2
  1. 1.Laboratory of Wind Power Control and Waste Energy Recovery, Research and Technology Center of EnergyBorj-Cedria, BP95 Hammam-LifTunisia
  2. 2.Energy and Thermal Systems Laboratory, National Engineering School of MonastirMonastirTunisia

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