Hostname: page-component-8448b6f56d-wq2xx Total loading time: 0 Render date: 2024-04-16T16:41:01.576Z Has data issue: false hasContentIssue false
  • English
  • Français

Evaluation of Three Lattice Boltzmann Models for Particulate Flows

Published online by Cambridge University Press:  03 June 2015

Liang Wang ,
Zhaoli Guo ,
Baochang Shi  and
Chuguang Zheng
Liang Wang*
Affiliation:
State Key Laboratory of Coal Combustion, Huazhong University of Science and Technology, Wuhan, 430074, P.R. China
Zhaoli Guo*
Affiliation:
State Key Laboratory of Coal Combustion, Huazhong University of Science and Technology, Wuhan, 430074, P.R. China
Baochang Shi*
Affiliation:
School of Mathematics and Statistics, Huazhong University of Science and Technology, Wuhan, 430074, P.R. China
Chuguang Zheng*
Affiliation:
State Key Laboratory of Coal Combustion, Huazhong University of Science and Technology, Wuhan, 430074, P.R. China
*
Email:zlguo@hust.edu.cn
Corresponding author.Email:wlsa0612@gmail.com
Email:shibc@hust.edu.cn
Email:cgzheng@mail.hust.edu.cn
Get access

Abstract

A comparative study is conducted to evaluate three types of lattice Boltzmann equation (LBE) models for fluid flows with finite-sized particles, including the lattice Bhatnagar-Gross-Krook (BGK) model, the model proposed by Ladd [Ladd AJC, J. Fluid Mech., 271, 285-310 (1994); Ladd AJC, J. Fluid Mech., 271, 311-339 (1994)], and the multiple-relaxation-time (MRT) model. The sedimentation of a circular particle in a two-dimensional infinite channel under gravity is used as the first test problem. The numerical results of the three LBE schemes are compared with the theoretical results and existing data. It is found that all of the three LBE schemes yield reasonable results in general, although the BGK scheme and Ladd’s scheme give some deviations in some cases. Our results also show that the MRT scheme can achieve a better numerical stability than the other two schemes. Regarding the computational efficiency, it is found that the BGK scheme is the most superior one, while the other two schemes are nearly identical. We also observe that the MRT scheme can unequivocally reduce the viscosity dependence of the wall correction factor in the simulations, which reveals the superior robustness of the MRT scheme. The superiority of the MRT scheme over the other two schemes is also confirmed by the simulation of the sedimentation of an elliptical particle.

Keywords

44.05.+e47.11.-j47.56.+rLattice Boltzmann equationfinite-sized particlesnumerical performancesedimentation in channel
Type
Research Article
Information
Communications in Computational Physics , Volume 13 , Issue 4 , April 2013 , pp. 1151 - 1172
Copyright
Copyright © Global Science Press Limited 2013

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.)

References

[1]Fung, Y. C., Biomechchanics Circulation, Springer-Verlag, Berlin, 1997.Google Scholar
[2]Smith, D. E., Babcock, H. P. and Chu, S., Single-polymer dynamics in steady shear flow, Science, 283 (1999), 1724–1727.Google Scholar
[3]Feng, J., Hu, H. H. and Joseph, D. D., Direct simulation of initial value problems for the motion of solid bodies in a Newtonian fluid: Part 1. Sedimentation, J. Fluid Mech., 261 (1994), 95–134.Google Scholar
[4]Feng, J., Hu, H. H. and Joseph, D. D., Direct simulation of initial value problems for the motion of solid bodies in a Newtonian fluid: Part 2. Couette and Poiseuille flows, J. Fluid Mech., 277 (1994), 271–301.CrossRefGoogle Scholar
[5]Patankar, N. A. and Joseph, D. D., Lagrangian numerical simulation of particulate flows, Int. J. Multiphase Flow, 27 (2001), 1685–1706.Google Scholar
[6]Patankar, N. A. and Joseph, D. D., Modeling and numerical simulation of particulate flows by the Eulerian-Lagrangian approach, Int. J. Multiphase Flow, 27 (2001), 1659–1684.CrossRefGoogle Scholar
[7]Benzi, R., Succi, S. and Vergassola, M. R., The lattice Boltzmann equation: theory and applications, Phys. Rep., 222 (1992), 145–197.CrossRefGoogle Scholar
[8]Chen, S. Y. and Doolen, G. D., Lattice Boltzmann method for fluid flows, Annu. Rev. Fluid Mech., 30 (1998), 329–364.CrossRefGoogle Scholar
[9]Succi, S., The Lattice Boltzmann Equation for Fluid Dynamics and Beyond, Oxford University Press, New York, 2001.CrossRefGoogle Scholar
[10]Ladd, A. J. C., Numerical simulations of particulate suspensions via a discretized Boltzmann equation, Part I. Theoretical foundation, J. Fluid Mech., 271 (1994), 285–310.Google Scholar
[11]Ladd, A. J. C., Numerical simulations of particulate suspensions via a discretized Boltzmann equation, Part II. Numerical results, J. Fluid Mech., 271 (1994), 311–339.CrossRefGoogle Scholar
[12]Aidun, C. K. and Lu, Y. N., Lattice Boltzmann simulation of solid particles suspended in fluid, J. Stat. Phys., 81 (1995), 49–61.CrossRefGoogle Scholar
[13]Aidun, C. K., Lu, Y. N. and Ding, E. J., Direct analysis of particulate suspensions with inertia using the discrete Boltzmann equation, J. Fluid Mech., 373 (1998), 287–311.CrossRefGoogle Scholar
[14]Qi, D. W., Lattice-Boltzmann simulations of particles in non-zero-Reynolds-number flows, J. Fluid Mech., 385 (1999), 41–62.CrossRefGoogle Scholar
[15]Feng, Z. G. and Michaelides, E. E., Interparticle forces and lift on a particle attached to a solid boundary in suspension flow, Phys. Fluids, 14 (2002), 49–60.Google Scholar
[16] A. Ladd, J. C. and Verberg, R., Lattice-Boltzmann simulation of particle-fluid suspensions, J. Stat. Phys., 104 (2001), 1191–1125.CrossRefGoogle Scholar
[17]Feng, Z. G. and Michaelides, E. E., Robust treatment of no-slip boundary condition and velocity updating for the lattice-Boltzmann simulation of particulate flows, Comput. Fluids, 38 (2009), 370–381.Google Scholar
[18]Wu, J. S. and Aidun, C. K., Simulating 3D deformable particle suspensions using lattice Boltz-mann method with discrete external boundary force, Int. J. Numer. Meth. Fluids, 62 (2010), 765–783.Google Scholar
[19]Lorenz, E., Caiazzo, A. and Hoekstra, A. G., Corrected momentum exchange method for lattice Boltzmann simulations of suspension flow, Phys. Rev. E, 79 (2009), 036705.Google Scholar
[20]Inamuro, T., Yoshino, M. and Ogino, F., A non-slip boundary conditions for lattice Boltzmann simulation, Phys. Fluids, 7 (1995), 2928–2930.Google Scholar
[21]Mei, R., Yu, D., Shyy, W. and Luo, L. S., Force evolution in the lattice Boltzmann method involving curved geometry, Phys. Rev. E, 65 (2002), 041203.Google Scholar
[22]Lallemand, P. and Luo, L. S., Lattice Boltzmann method for moving boundaries, J. Comput. Phys., 184 (2003), 406–421.CrossRefGoogle Scholar
[23]Ginzburg, I. and d’Humieres, D., Multireflection boundary conditions for lattice Boltzmann models, Phys. Rev. E, 68 (2003), 066614.CrossRefGoogle ScholarPubMed
[24]Cate, A. ten, Nieuwstad, C. H., Derksen, J. J. and Van den Akker, H. E. A., Particle imaging velocity experiments and lattice-Boltzmann simulations on a single sphere settling under gravity, Phys. Fluids, 14 (2002), 4012–4025.Google Scholar
[25]Owen, D. R. J., Leonardi, C. R. and Feng, Y.T., An efficient framework for fluidCstructure interaction using the lattice Boltzmann method and immersed moving boundaries, Int. J. Numer. Meth. Eng, 87 (2011), 66–95.Google Scholar
[26]Kollmannsberger, S., Geller, S., Duster, J.Tolke, A., Sorger, C., Krafczyk, M. and Rank, E., Fixed-grid fluid-structure interaction in two dimensions based on a partitioned Lattice Boltzmann and p-FEM approach, Int. J. Numer. Meth. Eng, 79 (2009), 817–845.Google Scholar
[27]Feng, Y. T., Han, K. and J Owen, D. R., Coupled lattice Boltzmann method and discrete element modelling of particle transport in turbulent fluid flows: Computational issues, Int. J. Numer. Meth. Eng, 72 (2007), 1111–1134.Google Scholar
[28]Feng, Y. T., Han, K. and Owen, D. R. J., Combined three-dimensional lattice Boltzmann meth-ods and discrete element method for modeling fluid-particle interactions with experiment assessment, Int. J. Numer. Meth. Eng, 81 (2010), 229–245.Google Scholar
[29]Peskin, C. S., Numerical analysis of blood flow in the heart, J. Comput. Phys., 25 (1977), 220–252.CrossRefGoogle Scholar
[30]Peskin, C. S., The immersed boundary method, Acta Numer., 11 (2002), 479–517.Google Scholar
[31]Feng, Z. G. and Michaelides, E. E., The immersed boundary-lattice Boltzmann method for solving fluid-particles interaction problem, J. Comput. Phys., 195 (2004), 602–628.CrossRefGoogle Scholar
[32]Feng, Z. G. and Michaelides, E. E., Proteus: a direct forcing method in the simulations of particulate flows, J. Comput. Phys., 202 (2005), 20–51.Google Scholar
[33]Niu, X. D., Shu, C., Chew, Y. T. and Peng, Y., A momentum exchange-based immersed boundary-lattice Boltzmann method for simulating incompressible viscous flows, Phys. Lett. A, 354 (2006), 173–182.Google Scholar
[34]Wu, J. and Shu, C., Particulate flow simulation via a boundary condition-enforced immersed boundary-lattice Boltzmann scheme, Commun. Comput. Phys., 7 (2010), 793–812.Google Scholar
[35]Cook, B. K., Noble, D. R. and Williams, J. R., A direct simulation method for particle-fluid systems, Eng. Computation, 21 (2004), 151–168.Google Scholar
[36]Shi, X. and Lim, S. P., A LBM-DLM/FD method for 3D fluid-structure interactions, J. Comput. Phys, 226 (2007), 2028–2043.CrossRefGoogle Scholar
[37]Rohde, M., Derksen, J. J. and van der Akker, H. E. A., An applicability study of advanced lattice-Boltzmann techniques for moving, no-slip boundaries and local grid refinement, Comput. Fluids, 37 (2008), 238–1252.Google Scholar
[38]Dupuis, A., Chatelain, P. and Koumoutsakos, P., An immersed boundary-lattice-Boltzmann method for the simulation of the flow past an impulsively started cylinder, J. Comput. Phys, 227 (2008), 4486–4498.Google Scholar
[39]Nie, D. M. and Lin, J. Z., A LB-DF/FD method for particle suspension, Commun. Comput. Phys., 7 (2010), 544–563.Google Scholar
[40]Peng, Y. and Luo, L. S., A comparative study of immersed-boundary and interpolated bounce-back methods in LBE, Prog. Comput. Fluid Dyna., 8 (2008), 156–167.CrossRefGoogle Scholar
[41] R. van der Sman, G. M., MRT Lattice Boltzmann schemes for confined suspension flows, Comput. Phys. Commun., 181 (2010), 1562–1569.Google Scholar
[42]Qian, Y. H., d’Humières, D. and Lallemand, P., Lattice BGK models for Navier-Stokes equation, Europhys. Lett., 17 (1992), 479–484.CrossRefGoogle Scholar
[43]Chen, H., Chen, S. and Matthaeus, W., Recovery of the Navier-Stokes equations through a lattice gas Boltzmann equation method, Phys. Rev. A, 45 (1992), 5339–5342.Google Scholar
[44]Frisch, U., d’Humieres, D., Hasslacher, B., Lallemand, P., Pomeau, Y. and Rivet, J.-P., nauattice gas hydrodynamics in two and three dimensions, Complex Syst., 1 (1987), 649–707.Google Scholar
[45]Lallemand, P. and Luo, L.S., Theory of the lattice Boltzmann method: Dispersion, dissipation, isotropy, Galilean invariance, and stability, Phys. Rev. E, 61 (2000), 6546–6562.CrossRefGoogle ScholarPubMed
[46]d’Humieres, D., Generalized lattice-Boltzmann equations, In: Shizgal, D.et al., editors. RGD, Prog. Astronaut. Aeronaut 159 (1992), 450–458.Google Scholar
[47]d’Humieres, D., Ginzburg, I., Krafczyk, M., Lallemand, P., Luo, L. S., Multiple-relaxation-time lattice Boltzmann models in three-dimensions, Phil. Trans. R. Soc. A, 360 (2002), 437–51.Google Scholar
[48]Lallemand, P. and Luo, L-S., Theory of the lattice Boltzmann method: acoustic and thermal properties in two and three dimensions, Phys. Rev. E, 68 (2003), 036706.CrossRefGoogle ScholarPubMed
[49]Wan, D. and Turek, S., Direct numerical simulation of particulate flow via multigrid FEM techniques and the fictitious boundary method, Int. J. Numer. Meth. Fluids, 51 (2006), 531–566.CrossRefGoogle Scholar
[50]Hu, H. H., Joseph, D. D. and Crochet, M. J., Direct simulation of fluid particle motions, Theo. Comput. Fluid Dyn., 3 (1992), 285–306.Google Scholar
[51]Li, H. B., Lu, X. Y., Fang, H. P. and Qian, Y. H., Force evolution in lattice Boltzmann simulations with moving boundaries in two dimensions, Phys. Rev. E, 70 (2004), 026701.Google Scholar
[52]Strack, O. E. and Cook, B. K., Three-dimensional immersed boundary conditions for moving solids in the lattice-Boltzmann method, Int. J. Numer. Meth. Fluids, 55 (2007), 103–125.Google Scholar
[53]Happel, J. and Brenner, H., Low Reynolds Number Hydrodynamics, Prentice-Hall, NewYork, 1965.Google Scholar
[54]Yu, Z. S. and Shao, X. M., A direct-forcing fictitious domain method for particulate flows, J. Comput. Phys., 227 (2007), 292–314.Google Scholar
[55]Guo, Z. L., Zheng, C. G. and Shi, B. C., An extrapolation method for boundary conditions in lattice Boltzmann method, Phys Fluids, 14 (2007), 2007–2010.Google Scholar
[56]Ginzburg, I. and Adler, P., Boundary flow condition analysis for the three-dimensional lattice Boltzmann model, J. Phys., II 4 (1994), 191–214.Google Scholar
[57]Ginzburg, I. and d’Humières, D., Local second-order boundary methods for lattice Boltzmann models, J. Stat. Phys, 84 (1996), 927–971.Google Scholar
[58]Pan, C., Luo, L. S. and Miller, C. T., An evaluation of lattice Boltzmann schemes for porous medium flow simulation, Comput. Fluid, 35 (2006), 898–909.CrossRefGoogle Scholar
[59]Huang, P., Hu, H., and Joseph, D., Direct simulation of the sedimentation of elliptic particles in Oldroyd-b fluids, J. Fluid Mech., 362 (1998), 297–325.Google Scholar
[60]Xia, Z. H., Connington, K. W., Papaka, S., Yue, P. T., Feng, J. J. and Chen, S. Y., Flow patterns in the sedimentation of an elliptical particle, J. Fluid Mech., 625 (2009), 249–272.Google Scholar