Volume 2, Issue 5, October 2017, Page: 47-51
Assessment of the Accuracy of the Multiple-Relaxation-Time Lattice Boltzmann Method for the Simulation of Circulating Flows
Mohammed Ahmed Boraey, Mechanical Power Engineering Department, Faculty of Engineering, Zagazig University, Zagazig, Egypt
Received: Sep. 23, 2017;       Accepted: Oct. 24, 2017;       Published: Nov. 20, 2017
DOI: 10.11648/j.mma.20170205.11      View  1732      Downloads  86
Abstract
The present work investigates the accuracy of the Multiple-relaxation-time Lattice Boltzmann Method (MRT LBM) in the simulation of flows with circulation. The flow in a 2Dlid-driven cavity is simulated using MRT LBM for a wide range of Reynolds numbers (100-1000) to assess its accuracy. The lid-driven cavity flow is selected because it is the standard benchmark problem for the testing of numerical methods. The calculated locations of the primary vortex center in addition to those of the two side vortices (lower-left and lower-right) are compared to the previously published results using different numerical techniques such as finite difference, finite element and single-relaxation-time LBM. The horizontal and vertical velocity profiles are also calculated. The results show that the MRT LBM has a superior accuracy compared to other numerical techniques especially for circulating flows.
Keywords
Multiple-Relaxation-Time, Numerical Accuracy, Lattice Boltzmann Method, Circulating Flow, Lid-Driven Cavity Flow
To cite this article
Mohammed Ahmed Boraey, Assessment of the Accuracy of the Multiple-Relaxation-Time Lattice Boltzmann Method for the Simulation of Circulating Flows, Mathematical Modelling and Applications. Vol. 2, No. 5, 2017, pp. 47-51. doi: 10.11648/j.mma.20170205.11
Copyright
Copyright © 2017 Authors retain the copyright of this article.
This article is an open access article distributed under the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0/) which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Reference
[1]
Witherden, F. D. and A. Jameson. Future Directions of Computational Fluid Dynamics. In 23rd AIAA Computational Fluid Dynamics Conference. 2017.
[2]
Li, Y., et al., Coupled computational fluid dynamics/multibody dynamics method for wind turbine aero-servo-elastic simulation including drive train dynamics. Renewable Energy, 2017.101: p. 1037-1051.
[3]
Rutkowski, D. R., et al., Surgical planning for living donor liver transplant using 4D flow MRI, computational fluid dynamics and in vitro experiments. Computer Methods in Biomechanics and Biomedical Engineering: Imaging & Visualization, 2017: p.1-11.
[4]
Fortunato, L., et al., In-situ assessment of biofilm formation in submerged membrane system using optical coherence tomography and computational fluid dynamics. Journal of Membrane Science, 2017.521: p.84-94.
[5]
Boulard, T., et al., Modelling of micro meteorology, canopy transpiration and photosynthesis in a closed green house using computational fluid dynamics. Biosystems Engineering, 2017. 158: p.110-133.
[6]
Tao, Y., K. Inthavong, and J. Tu, Computational fluid dynamics study of human-induced wake and particle dispersion in indoor environment. Indoor and Built Environment, 2017.26(2): p.185-198.
[7]
Chen, S. and G. D. Doolen, LATTICE BOLTZMANN METHOD FOR FLUID FLOWS. Annual Review of Fluid Mechanics, 1998.30(1): p.329-364.
[8]
Perumal, D. A. and A. K. Dass, Application of Lattice Boltzmann method for incompressible viscous flows. Applied Mathematical Modelling, 2013.37(6): p.4075-4092.
[9]
He, Y., et al., Lattice Boltzmann method and its applications in engineering thermophysics. Chinese Science Bulletin, 2009.54(22): p.4117.
[10]
Li, Q., et al., Lattice Boltzmann methods for multiphase flowand phase-change heat transfer. Progress in Energy and Combustion Science, 2016.52: p.62-105.
[11]
Bao, J. and L. Schaefer, Lattice Boltzmann equation model for multi-component multi-phase flow with high density ratios. Applied Mathematical Modelling, 2013.37(4): p.1860-1871.
[12]
Psihogios, J., et al., A Lattice Boltzmann study of non-newtonian flow in digitally reconstructed porous domains. Transport in Porous Media, 2007.70(2): p.279-292.
[13]
Wang, C.-H. and J.-R. Ho, A lattice Boltzmann approach for the non-Newtonian effect in the blood flow. Computers & Mathematics with Applications, 2011.62(1): p.75-86.
[14]
Hao, J. and L. Zhu, A lattice Boltzmann based implicit immersed boundary method for fluid–structure interaction. Computers & Mathematics with Applications, 2010.59(1): p.185-193.
[15]
Yang, J. and E. S. Boek, A comparison study of multi-component Lattice Boltzmann models for flow in porous media applications. Computers & Mathematics with Applications, 2013.65(6): p.882-890.
[16]
Fakhari, A., D. Bolster, and L.-S. Luo, A weighted multiple-relaxation-time lattice Boltzmann method for multiphase flows and its application to partial coalescence cascades. Journal of Computational Physics, 2017.341: p.22-43.
[17]
Zhuo, C. and P. Sagaut, Acoustic multipole sources for the regularized Lattice Boltzmann method: Comparison with multiple-relaxation-time models in the inviscid limit. Physical Review E, 2017.95(6): p.063301.
[18]
Hu, Y., et al., A multiple-relaxation-time lattice Boltzmann model for the flow and heat transfer in a hydrodynamically and thermally anisotropic porous medium. International Journal of Heat and Mass Transfer, 2017.104: p.544-558.
[19]
Liu, Q., Y.-L. He, and Q. Li, Enthalpy-based multiple-relaxation-time lattice Boltzmann method for solid-liquid phase-change heat transfer in metal foams. Physical Review E, 2017.96(2): p.023303.
[20]
Mahmood, R., et al., Numerical Simulations of the Square Lid Driven Cavity Flow of Bingham Fluids Using Nonconforming Finite Elements Coupled with a Direct Solver. Advances in Mathematical Physics, 2017.2017.
[21]
Abu-Nada, E. and A. J. Chamkha, Mixed convection flow of a nanofluid in a lid-driven cavity with a wavy wall. International Communications in Heat and Mass Transfer, 2014.57: p.36-47.
[22]
Botella, O. and R. Peyret, Benchmark spectral results on the lid-driven cavity flow. Computers & Fluids, 1998.27(4): p.421-433.
[23]
Grillet, A. M., et al., Modeling of viscoelastic lid driven cavity flow using finite element simulations. Journal of Non-Newtonian Fluid Mechanics, 1999.88(1): p.99-131.
[24]
Benyahia, S., et al., Simulation of particles and gas flow behavior in the riser section of a circulating fluidized bed using the kinetic theory approach for the particulate phase. Powder Technology, 2000.112(1): p.24-33.
[25]
Alex, J., et al., Analysis and design of suitable model structures for activated sludge tanks with circulating flow. Water science and technology, 1999.39(4): p.55-60.
[26]
Bhatnagar, P. L., E. P. Gross, and M. Krook, A model for collision processes in gases. I. Small amplitude processes in charged and neutral one-component systems. Physical review, 1954.94(3): p.511.
[27]
Vanka, S. P., Block-implicit multigrid solution of Navier-Stokes equations in primitive variables. Journal of Computational Physics, 1986.65(1): p.138-158.
[28]
Ghia, U., K. N. Ghia, and C. T. Shin, High-Resolutions for incompressible flow using the Navier-Stokes equations and a multigrid method. Journal of Computational Physics, 1982.48(3): p.387-411.
[29]
Hou, S., et al., Simulation of Cavity Flow by the Lattice Boltzmann Method. Journal of Computational Physics, 1995.118(2): p.329-347.
[30]
Schreiber, R. and H. B. Keller, Driven cavity flows by efficient numerical techniques. Journal of Computational Physics, 1983.49(2): p.310-333.
[31]
Gupta, M. M. and J. C. Kalita, A new paradigm for solving Navier–Stokes equations: stream function–velocity formulation. Journal of Computational Physics, 2005.207(1): p. 52-68.
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