Hostname: page-component-76c49bb84f-sz5hq Total loading time: 0 Render date: 2025-07-13T09:28:21.112Z Has data issue: false hasContentIssue false
  • English
  • Français

Lattice Boltzmann method for direct numerical simulation of turbulent flows

Published online by Cambridge University Press:  08 July 2010

S. S. CHIKATAMARLA ,
C. E. FROUZAKIS ,
I. V. KARLIN ,
A. G. TOMBOULIDES  and
K. B. BOULOUCHOS
S. S. CHIKATAMARLA*
Affiliation:
LAV, Institute of Energy Technology, ETH Zurich, 8092 Zurich, Switzerland
C. E. FROUZAKIS
Affiliation:
LAV, Institute of Energy Technology, ETH Zurich, 8092 Zurich, Switzerland
I. V. KARLIN
Affiliation:
LAV, Institute of Energy Technology, ETH Zurich, 8092 Zurich, Switzerland School of Engineering Sciences, University of Southampton, Southampton SO17 1BJ, UK
A. G. TOMBOULIDES
Affiliation:
Department of Mechanical Engineering, University of Western Macedonia, 50100 Kozani, Greece
K. B. BOULOUCHOS
Affiliation:
LAV, Institute of Energy Technology, ETH Zurich, 8092 Zurich, Switzerland
*
†Email address for correspondence: shyam_css@yahoo.com
Get access Rights & Permissions [Opens in a new window]

Abstract

We present three-dimensional direct numerical simulations (DNS) of the Kida vortex flow, a prototypical turbulent flow, using a novel high-order lattice Boltzmann (LB) model. Extensive comparisons of various global and local statistical quantities obtained with an incompressible-flow spectral element solver are reported. It is demonstrated that the LB method is a promising alternative for DNS as it quantitatively captures all the computed statistics of fluid turbulence.

JFM classification

Mathematical Foundations: Computational methods Turbulent Flows: Isotropic turbulence Turbulent Flows: Turbulence simulation

Information

Type
Papers
Information
Journal of Fluid Mechanics , Volume 656 , 10 August 2010 , pp. 298 - 308
Copyright
Copyright © Cambridge University Press 2010

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Article purchase

Temporarily unavailable

References

REFERENCES

Ansumali, S. & Karlin, I. V. 2005 Consistent lattice Boltzmann method. Phys. Rev. Lett. 95, 260605.CrossRefGoogle ScholarPubMed
Ansumali, S., Karlin, I. V., Arcidiacono, S., Abbas, A. & Prasianakis, N. I. 2007 Hydrodynamics beyond Navier–Stokes: exact solution to the lattice Boltzmann hierarchy. Phys. Rev. Lett. 98, 124502.CrossRefGoogle Scholar
Ansumali, S., Karlin, I. V. & Öttinger, H. C. 2003 Minimal entropic kinetic models for simulating hydrodynamics. Europhys. Lett. 63, 798–804.CrossRefGoogle Scholar
Arcidiacono, S., Karlin, I. V., Mantzaras, J. & Frouzakis, C. E. 2007 Lattice Boltzmann model for the simulation of multi-component mixtures. Phys. Rev. E 76, 046703.CrossRefGoogle Scholar
Benzi, R. & Succi, S. 1990 Two-dimensional turbulence with the lattice Boltzmann equation. J. Phys. A 23 (1), L1–L5.CrossRefGoogle Scholar
Benzi, R., Succi, S. & Vergassola, M. 1992 The lattice Boltzmann equation: theory and applications. Phys. Rep. 222, 145–197.CrossRefGoogle Scholar
Boratav, O. N. & Pelz, R. B. 1994 Direct numerical simulation of transition to turbulence from a high-symmetry initial condition. Phys. Fluids 6, 2757.CrossRefGoogle Scholar
Brachet, M. E. 1991 Direct simulation of three-dimensional turbulence in the Taylor–Green vortex. Fluid Dyn. Res. 8, 1.CrossRefGoogle Scholar
Chikatamarla, S. S., Ansumali, S. & Karlin, I. V. 2006 Entropic lattice Boltzmann models for hydrodynamic in three dimensions. Phys. Rev. Lett. 97, 010201.CrossRefGoogle ScholarPubMed
Chikatamarla, S. S. & Karlin, I. V. 2006 Entropic and Galilean invariance of lattice Boltzmann theories. Phys. Rev. Lett. 97, 090601.CrossRefGoogle Scholar
Chikatamarla, S. S. & Karlin, I. V. 2009 Lattices for the lattice Boltzmann method. Phys. Rev. E. 79, 046701.CrossRefGoogle ScholarPubMed
Hazi, G. & Kavran, P. 2006 On the cubic velocity deviations in lattice Boltzmann methods. J. Phys. A: Math. Gen. 39 (12), 3127–3136.CrossRefGoogle Scholar
Karlin, I. V., Ferrante, A. & Ottinger, H. C. 1999 Perfect entropy functions of the lattice Boltzmann method. Europhys. Lett. 47, 182–188.CrossRefGoogle Scholar
Karniadakis, G. E., Israeli, M. & Orszag, S. A. 1991 High-order splitting methods for the incompressible Navier–Stokes equations. J. Comput. Phys. 97, 414.CrossRefGoogle Scholar
Keating, B., Vahala, G., Yepez, J., Soe, M. & Vahala, L. 2007 Entropic lattice Boltzmann representations required to recover Navier–Stokes flows. Phys. Rev. E 75, 036712.CrossRefGoogle ScholarPubMed
Kida, S. 1985 Three-dimensional periodic flows with high-symmetry. J. Phys. Soc. Japan 54, 2132.CrossRefGoogle Scholar
Kida, S. & Murakami, Y. 1987 Kolmogorov similarity in freely decaying turbulence. Phys. Fluids 30, 2030.CrossRefGoogle Scholar
Kolmogorov, A. N. 1941 The local structure of turbulence in an incompressible fluid with very large Reynolds number. C. R. Acad. Sci. 30, 301.Google Scholar
McNamara, G. R., Garcia, A. L. & Alder, B. J. 1995 Stabilization of thermal Lattice Boltzmann models. J. Stat. Phys. 81, 395–408.CrossRefGoogle Scholar
Mei, R., Luo, L. S., Lallemand, P. & d'Humieres, D. 2006 Consistent initial conditions for lattice Boltzmann simulations. Comput. Fluids 35, 855–862.CrossRefGoogle Scholar
Orszag, S. A. 1983 Numerical simulation of the Taylor–Green vortex. Proc. Symp. Comput. Method. Appl. Sci. Engng 50, 50.Google Scholar
Patera, A. T. 1984 A spectral element method for fluid dynamics: laminar flow in a channel expansion. J. Comput. Phys. 54, 468–488.CrossRefGoogle Scholar
Philippi, P. C., Hegele, L. A. Jr, Dos Santos, L. O. & Surmas, R. 2006 From the continuous to the lattice Boltzmann equation: the discretization problem and thermal models. Phys. Rev. E 73 (5 Pt 2), 056702.CrossRefGoogle Scholar
Qian, Y. H. & Orszag, S. A. 1993 Lattice BGK models for the Navier–Stokes equation: nonlinear deviation in compressible regimes. Europhys. Lett. 21, 255–259.CrossRefGoogle Scholar
Qian, Y.-H. & Zhou, Y. 1998 Complete Galilean-invariant lattice BGK models for the Navier–Stokes equation. Europhys. Lett. 42 (4), 359–364.CrossRefGoogle Scholar
Shan, X. W. & He, X. 1998 Discretization of the velocity space in the solution of the Boltzmann equation. Phys. Rev. Lett. 80, 65.CrossRefGoogle Scholar
Shan, X. W., Yuan, X. & Chen, H. 2006 Kinetic theory representation of hydrodynamics: a way beyond the Navier—Stokes equation. J. Fluid Mech. 550, 413–441.CrossRefGoogle Scholar
Succi, S. 2001 The Lattice Boltzmann Equation for Fluid Dynamics and Beyond. Oxford University Press.CrossRefGoogle Scholar
Swift, M. R., Orlandini, E., Osborn, W. R. & Yeomans, J. M. 1996 Lattice Boltzmann simulations of liquid-gas and binary fluid systems. Phys. Rev. E 54, 5041.CrossRefGoogle ScholarPubMed
Tomboulides, A. G., Israeli, M. & Karniadakis, G. E. 1989 Efficient removal of boundary-divergence errors in time-splitting methods. J. Sci. Comput. 4, 291.CrossRefGoogle Scholar