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Simulation of Turbulent Flows Using a Finite-Volume Based Lattice Boltzmann Flow Solver

Published online by Cambridge University Press:  28 November 2014

Goktan Guzel  and
Ilteris Koc
Goktan Guzel*
Affiliation:
ASELSAN Inc, MGEO Division, Etlik 06011, Ankara, Turkey
Ilteris Koc
Affiliation:
ASELSAN Inc, MGEO Division, Etlik 06011, Ankara, Turkey
*
*Email addresses:[email protected](G. Guzel), [email protected](I. Koc)
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Abstract

In this study, the Lattice Boltzmann Method (LBM) is implemented through a finite-volume approach to perform 2-D, incompressible, and turbulent fluid flow analyses on structured grids. Even though the approach followed in this study necessitates more computational effort compared to the standard LBM (the so called stream and collide scheme), using the finite-volume method, the known limitations of the stream and collide scheme on lattice to be uniform and Courant-Friedrichs-Lewy (CFL) number to be one are removed. Moreover, the curved boundaries in the computational domain are handled more accurately with less effort. These improvements pave the way for the possibility of solving fluid flow problems with the LBM using coarser grids that are refined only where it is necessary and the boundary layers might be resolved better.

Keywords

76M1276M2876D9976F99Lattice Boltzmann Methodfinite-volume approachturbulent flows
Type
Research Article
Information
Communications in Computational Physics , Volume 17 , Issue 1 , January 2015 , pp. 213 - 232
Copyright
Copyright © Global Science Press Limited 2015 

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References

[1]Frisch, U., Hasslacher, B. and Pomeau, Y., Lattice-gas automata for the Navier-Stokes equation, Phys. Rev. Lett., 56 (1986), 1505–1508.CrossRefGoogle ScholarPubMed
[2]Thömmes, G., Becker, J., Junk, M., Vaikuntam, A. and Kehrwald, D., A Lattice Boltzmann Method for immiscible multiphase flow simulations using the level set method, J. Comput. Phys., 228 (2009), 1139–1156.Google Scholar
[3]Li, X. M., Leung, R. C. K. and So, R. M. C., One-step aeroacoustics simulation using Lattice Boltzmann Method, AIAA J., 44 (2006), 79–89.Google Scholar
[4]Chen, S., A Large-Eddy based Lattice Boltzmann Model for turbulent flow simulation, Appl. Math. Comput., 215 (2009), 591–598.Google Scholar
[5]Fallah, M. A., Myles, V. M., Krüger, T., Sritharan, K., Wixforth, A., Varnik, F., Schneider, S. W. and Schneider, M. F., Acoustic driven flow and Lattice Boltzmann Simulations to study cell adhesion in biofunctionalized μ-fluidic channels with complex geometry, Biomicrofluidics, 4 (2010), 024106.Google Scholar
[6]He, X. Y., Luo, L. S., and Dembo, M., Some progress in Lattice-Boltzmann Methods. Part 1. Nonuniform mesh grids, J. Comput. Phys., 129 (1996), 357–363.Google Scholar
[7]Filippova, O. and Hanel, D., Boundary-fitting and local grid refinement for Lattice BGK Models, Int. J. Mod. Phys. C, 9 (1998), 1271–1279.CrossRefGoogle Scholar
[8]Succi, S., Amati, G. and Benzi, R., Challenges in Lattice Boltzmann computing, J. Stat. Phys., 81 (1995), 5–16.CrossRefGoogle Scholar
[9]Bhatnagar, P. L., Gross, E. P. and Krook, M., A model for collision processes in gases, Phys. Rev. Lett., 94 (1954), 511–525.Google Scholar
[10]He, X. Y. and Luo, L. S., Lattice Boltzmann Model for the incompressible Navier-Stokes equation, J. Stat. Phys., 88 (1997), 927–944.CrossRefGoogle Scholar
[11]Peng, G., Xi, H., Duncan, C. and Chou, S. H., Finite volume scheme for the Lattice Boltzmann Method on unstructured meshes, Phys. Rev. E, 59 (1999), 4675–4682.Google Scholar
[12]Stiebler, M., Tolke, J. and Krafczyk, M., An upwind scheme for the finite volume Lattice Boltzmann Method, Comput. Fluids, 35 (2006), 814–819.Google Scholar
[13]Patil, D. V. and Lakshmisha, K. N., Finite volume TVD formulation of Lattice Boltzmann simulation on unstructured mesh, J. Comput. Phys., 228 (2009), 5262–5279.CrossRefGoogle Scholar
[14]Zarghami, A., Maghrebi, M. J., Ghasemi, J. and Ubertini, S., Lattice Boltzmann finite volume formulation with improved stability, Commun. Comput. Phys., 12 (2012), 42–64.CrossRefGoogle Scholar
[15]Van Leer, B., Towards the Ultimate Conservative Difference Scheme. V. A second order sequel to Godunov's method, J. Comput. Phys., 32 (1979), 101–136.Google Scholar
[16]Pareschi, S. and Russo, G., Implicit-explicit Runge-Kutta schemes and applications to hyperbolic systems with relaxation, J. Sci. Comput., 25 (2005), 129–155.Google Scholar
[17]Wang, Y., He, Y. L., Zhao, T. S., Tang, G. H. and Tao, W. Q., Implicit-explicit finite-difference Lattice-Boltzmann Method for compressible flows, Int. J. Mod. Phys. C, 18 (2007), 1961–1983.CrossRefGoogle Scholar
[18]Guo, Z., Zheng, C. and Shi, B., An extrapolation method for boundary conditions in Lattice Boltzmann Method, Phys. Fluids, 14 (2002), 2007–2010.CrossRefGoogle Scholar
[19]Spalart, P. R. and Allmaras, S. R., A one-equation turbulence model for aerodynamic flows, AIAA Pap., AIAA-92-0439, 1992.Google Scholar
[20]Ghia, U., Ghia, K. N. and Shin, C. T., High-resolutions for incompressible flow using the Navier-Stokes Equations and a multigrid method, J. Comput. Phys., 48 (1982), 387–411.Google Scholar
[21]White, F. M., Viscous Fluid Flow, 2nd ed., Chap. 4, McGraw-Hill, 1991.Google Scholar
[22]Blazek, J., Computational Fluid Dynamics: Principles and Applications, Chap. 11, Elsevier, 2001.Google Scholar
[23]Nieuwstadt, F. and Keller, H. B., Viscous flow past circular cylinders, Comput. Fluids, 1 (1973), 59–71.Google Scholar
[24]Coutanceau, M. and Bouard, R., Experimental determination of the main features of the viscous flow in the wake of a circular cylinder in uniform translation. Part 1: Steady flow, J. Fluid Mech., 79 (1977), 231–256.CrossRefGoogle Scholar
[25]He, X. and Doolen, G., Lattice Boltzmann Method on curvilinear coordinates system: Flow around a circular cylinder, J. Comput. Phys., 134 (1997), 306–315.Google Scholar
[26]Mei, R. W. and Shyy, W., On the finite difference-based Lattice Boltzmann Method in curvilinear coordinates, J. Comput. Phys., 143 (1998), 426–448.Google Scholar
[27]Ladson, C. L., Effect of independent variation of Mach and Reynolds numbers on the low-speed aerodynamic of the NACA 0012 airfoil section, NASA TM-4074, 1988.Google Scholar
[28]Gregory, N. and O'Reilly, C. L., Low-speed aerodynamic characteristics of NACA 0012 aerofoil section, including the effects of upper-surface roughness simulation hoar frost, NASA RM-3726, 1970.Google Scholar