×

Numerical simulation of viscous flow over a square cylinder using lattice Boltzmann method. (English) Zbl 1360.76089

Summary: This work is concerned with the lattice Boltzmann computation of two-dimensional incompressible viscous flow past a square cylinder confined in a channel. It is known that the nature of the flow past cylindrical obstacles is very complex. In the present work, computations are carried out both for steady and unsteady flows using lattice Boltzmann method. Effects of Reynolds number, blockage ratio, and channel length are studied in detail. As good care has been taken to include appropriate measures in the computational method, these results enjoy good credibility. To sum up, the present study reveals many interesting features of square cylinder problem and demonstrates the capability of the lattice Boltzmann method to capture these features.

MSC:

76D17 Viscous vortex flows
76M28 Particle methods and lattice-gas methods
Full Text: DOI

References:

[1] R. W. Davis, E. F. Moore, and L. P. Purtell, “A numerical-experimental study of confined flow around rectangular cylinders,” Physics of Fluids, vol. 27, no. 1, pp. 46-59, 1984. · doi:10.1063/1.864486
[2] R. Franke, W. Rodi, and B. Schönung, “Numerical calculation of laminar vortex shedding flow past cylinders,” Journal of Wind Engineering and Industrial Aerodynamics, vol. 35, pp. 237-257, 1990. · doi:10.1016/0167-6105(90)90219-3
[3] A. Mukhopadhyay, G. Biswas, and T. Sundararajan, “Numerical investigation of confined wakes behind a square cylinder in a channel,” International Journal for Numerical Methods in Fluids, vol. 14, no. 12, pp. 1473-1484, 1992. · Zbl 0825.76163 · doi:10.1002/fld.1650141208
[4] H. Suzuki, K. Fukutani, T. Takishita, and K. Suzuki, “Unsteady flow in a channel obstructed by a square rod (crisscross motion of vortex),” International Journal of Heat Fluid Flow, vol. 14, no. 1, pp. 2-9, 1993. · doi:10.1016/0142-727X(93)90034-K
[5] A. Sohankar, C. Norberg, and L. Davidson, “Numerical simulation of unsteady low-reynolds number flow around rectangular cylinders at incidence,” Journal of Wind Engineering and Industrial Aerodynamics, vol. 69, pp. 189-201, 1997. · doi:10.1016/S0167-6105(97)00154-2
[6] A. Sohankar, C. Norberg, and L. Davidson, “Low-Reynolds-number flow around a square cylinder at incidence: study of blockage, onset of vortex shedding and outlet 21 boundary condition,” International Journal for Numerical Methods in Fuids, vol. 26, pp. 39-56, 1998. · Zbl 0910.76067 · doi:10.1002/(SICI)1097-0363(19980115)26:1<39::AID-FLD623>3.0.CO;2-P
[7] A. N. Pavlov, S. S. Sazhin, R. P. Fedorenko, and M. R. Heikal, “A conservative finite difference method and its application for the analysis of a transient flow around a square prism,” International Journal of Numerical Methods for Heat & Fluid Flow, vol. 10, no. 1, pp. 6-46, 2000. · Zbl 0966.76061 · doi:10.1108/09615530010306894
[8] M. Breuer, J. Bernsdorf, T. Zeiser, and F. Durst, “Accurate computations of the laminar flow past a square cylinder based on two different methods: lattice-Boltzmann and finite-volume,” International Journal of Numerical Methods for Heat & Fluid Flow, vol. 21, no. 2, pp. 186-196, 2000. · doi:10.1016/S0142-727X(99)00081-8
[9] D. C. Wan, B. S. V. Patnaik, and G. W. Wei, “Discrete singular convolution-finite subdomain method for the solution of incompressible viscous flows,” Journal of Computational Physics, vol. 180, no. 1, pp. 229-255, 2002. · Zbl 1130.76403 · doi:10.1006/jcph.2002.7089
[10] A. Roy and G. Bandyopadhyay, “Numerical investigation of confined flow past a square cylinder placed in a channel,” in Proceedings of the All-India Seminar on Aircrafts and Trans-atmospheric Vehicles: Missions, Challenges and Perspectives, pp. 28-29, Kolkata, May 2004.
[11] S. Abide and S. Viazzo, “A 2D compact fourth-order projection decomposition method,” Journal of Computational Physics, vol. 206, no. 1, pp. 252-276, 2005. · Zbl 1087.76083 · doi:10.1016/j.jcp.2004.12.005
[12] N. Hasan, S. F. Anwer, and S. Sanghi, “On the outflow boundary condition for external incompressible flows: a new approach,” Journal of Computational Physics, vol. 206, no. 2, pp. 661-683, 2005. · Zbl 1120.76306 · doi:10.1016/j.jcp.2004.12.025
[13] K. M. Kelkar and S. V. Patankar, “Numerical prediction of vortex shedding behind a square cylinder,” International Journal for Numerical Methods in Fluids, vol. 14, no. 3, pp. 327-341, 1992. · Zbl 0746.76066 · doi:10.1002/fld.1650140306
[14] S. Hou, Q. Zou, S. Chen, G. Doolen, and A. C. Cogley, “Simulation of cavity flow by the Lattice Boltzmann method,” Journal of Computational Physics, vol. 118, pp. 329-347, 1995. · Zbl 0821.76060 · doi:10.1006/jcph.1995.1103
[15] D. A. Perumal and A. K. Dass, “Multiplicity of steady solutions in two-dimensions lid-driven cavity flows by Lattice Boltzmann method,” Computers & Mathematics with Applications, vol. 61, no. 12, pp. 3711-3721, 2011. · Zbl 1225.76240 · doi:10.1016/j.camwa.2010.03.053
[16] D. Yu, R. Mei, L. S. Luo, and W. Shyy, “Viscous flow computations with the method of Lattice Boltzmann equation,” Progress in Aerospace Sciences, vol. 39, no. 5, pp. 329-367, 2003. · doi:10.1016/S0376-0421(03)00003-4
[17] M. Bouzidi, M. Firdaouss, and P. Lallamand, “Momentum transfer of a Lattice Boltzmann fluid with boundaries,” Physics of Fluids, vol. 13, no. 11, pp. 3452-3459, 2001. · Zbl 1184.76068 · doi:10.1063/1.1399290
[18] G. V. S. Kumar, D. A. Perumal, and A. K. Dass, “Numerical simulation of viscous flow over a circular cylinder using Lattice Boltzmann method,” in Proceedings of the International Conference on Fluid Mechanics and Fluid Power, IIT Madras, India, December 2010.
[19] D. J. Tritton, “Experiments on the flow past a circular cylinder at low reynolds numbers,” Journal of Fluid Mechanics, vol. 6, no. 4, pp. 547-567, 1959. · Zbl 0092.19502 · doi:10.1017/S0022112059000829
[20] B. A. Fornberg, “A numerical study of steady viscous flow past a circular cylinder,” Journal of Fluid Mechanics, vol. 98, no. 4, pp. 819-855, 1980. · Zbl 0428.76032 · doi:10.1017/S0022112080000419
[21] D. Calhoun, “A Cartesian grid method for solving the two-dimensional streamfunction-vorticity equations in irregular regions,” Journal of Computational Physics, vol. 176, no. 2, pp. 231-275, 2002. · Zbl 1130.76371 · doi:10.1006/jcph.2001.6970
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.