Title

Using the lid-driven cavity flow to validate moment-based boundary conditions for the lattice Boltzmann equation

Journal title

Archive of Mechanical Engineering

Yearbook

2017

Volume

vol. 64

Issue

No 1

Affiliation

Mohammed, Seemaa : School of Computing Electronics and Mathematics, Plymouth University, UK ; Reis, Tim : Department of Mathematical Sciences, University of Greenwich, UK

Authors

Mohammed, Seemaa ; Reis, Tim

Keywords

lattice Boltzmann equation ; moment-based boundary conditions ; multiple relaxation times

Divisions of PAS

Nauki Techniczne

Coverage

57-74

Publisher

Polish Academy of Sciences, Committee on Machine Building

Bibliography

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[7] P.J. Dellar. Incompressible limits of lattice Boltzmann equations using multiple relaxation times. J. Comput. Phys., 190:351–370, 2003.
[8] A. JC. Ladd. Numerical simulations of particulate suspensions via a discretized Boltzmann equation. part 1. theoretical foundation. J. Fluid Mech., 271:285–309, 1994.
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[11] I. Ginzbourg and P.M. Adler. Boundary flow condition analysis for the three-dimensional lattice Boltzmann model. J. Phys. II. France, 4:191–214, 1994.
[12] J.E. Broadwell. Study of rarefied shear flow by the discrete velocity method. J. Fluid Mech., 19:401–414, 1964.
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[16] S. Bennett. A lattice Boltzmann model for diffusion of binary gas mixtures. PhD thesis, University of Cambridge, 2010.
[17] D.R. Noble, S. Chen, G. Georgiadis, and R.O. Buckius. A consistent hydrodynamic boundary condition for the lattice Boltzmann method. Phys. Fluids, 7(1):203–209, 1995.
[18] S. Bennett, P. Asinari, and P.J. Dellar. A lattice Boltzmann model for diffusion of binary gas mixtures that includes diffusion slip. I nt. J. Numer. Meth. Fluids, 69:171–189, 2012.
[19] R. Allen and T. Reis. Moment-based boundary conditions for lattice Boltzmann simulations of natural convection in cavities. Prog. Comp. Fluid Dyn.: An Int. J., 16:216–231, 2016.
[20] T. Reis and P.J. Dellar. Moment-based formulation of Navier–Maxwell slip boundary conditions for lattice Boltzmann simulations of rarefied flows in microchannels. Phys. Fluids, 2012.
[21] A. Hantsch, T. Reis, and U. Gross. Moment method boundary conditions for multiphase lattice Boltzmann simulations with partially-wetted walls. Int. J. Multiphase Flow, 7:1–14, 2015.
[22] U. Ghia, K.N. Ghia, and C.T. Shin. High-resolutions for incompressible flow using the Navier- Stokes equations and a multigrid method. J. Comput. Phys., 48:387–411, 1982.
[23] M. Sahin and R.G. Owens. A novel fully implicit finite volume method applied to the lid-driven cavity problem—part i: High Reynolds number flow calculations. Int. J. Numer. Meth. Fluids, 42:57–77, 2003.
[24] O. Botella and R. Peyret. Benchmark spectral results on the lid-driven cavity flow. Comput. Fluids, 27:421–433, 1998.
[25] S. Hou, Q. Zou, G.D. Chen, S.and Doolen, and A.C. Cogley. Simulation of cavity flow by the lattice Boltzmann method. J. Comput. Phys., 118:329–347, 1995.
[26] M.A. Mussa, S.Abdullah, C.S.N. Azwadi,N. Muhamad, K. Sopian, S. Kartalopoulos, A. Buikis, N. Mastorakis, and L. Vladareanu. Numerical simulation of lid-driven cavity flow using the lattice Boltzmann method. In WSEAS International Conference. Proceedings. Mathematics and Computers in Science and Engineering. WSEAS, 2008.
[27] L.S. Luo,W. Liao, X. Chen,Y. Peng,W. Zhang, et al. Numerics of the lattice Boltzmann method: Effects of collision models on the lattice Boltzmann simulations. Phys. Rev. E, 83(5):056710, 2011.
[28] X. He, X. Shan, and G.D. Doolen. Discrete Boltzmann equation model for nonideal gases. Phys. Rev. E, 57:R13, 1998.
[29] R. Benzi, S. Succi, and M. Vergassola. Turbulence modelling by nonhydrodynamic variables. Europhys. Lett., 13:727, 1990.
[30] P. J Dellar. Nonhydrodynamic modes and a priori construction of shallow water lattice Boltzmann equations. Phys. Rev. E, 65:036309, 2002.
[31] J. Latt and B. Chopard. Lattice Boltzmann method with regularized pre-collision distribution functions. Comput. Fluid., 72:165–168, 2006.
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[33] S. Hou, Q. Zou, S. Chen, G. D. Doolen, and A.C. Cogley. Simulation of cavity flow by the lattice boltzmann method. J. Comp. Phys., 118(2)(2):329 –347, 1995.
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Date

2017

Type

Artykuły / Articles

Identifier

DOI: 10.1515/meceng-2017-0004 ; ISSN 0004-0738, e-ISSN 2300-1895

Source

Archive of Mechanical Engineering; 2017; vol. 64; No 1; 57-74

References

Hou (1995), Simulation of cavity flow by the lattice boltzmann method, Phys, 118, 329. ; Hou (1995), and Doolen Simulation of cavity flow by the lattice Boltzmann method, Comput Phys, 118, 329, doi.org/10.1006/jcph.1995.1103 ; Hantsch (2015), Moment method boundary conditions for multiphase lattice Boltzmann simulations with partially - wetted walls Multiphase Flow, Int J, 7, 1. ; Bennett (2012), A lattice Boltzmann model for diffusion of binary gas mixtures that includes diffusion slip Fluids, Int J, 69. ; Gatignol (1988), Kinetic theory boundary conditions for discrete velocity gases, Phys Fluids, 20, 1958. ; Dellar (2002), Nonhydrodynamic modes and a priori construction of shallow water lattice Boltzmann equations, Phys Rev, 65, 036309. ; Broadwell (1964), Study of rarefied shear flow by the discrete velocity method, Fluid Mech, 19, 401, doi.org/10.1017/S0022112064000817 ; Ginzbourg (1994), Boundary flow condition analysis for the three - dimensional lattice Boltzmann model, Phys II, 4, 191. ; Dellar (2003), Incompressible limits of lattice Boltzmann equations using multiple relaxation times, Comput Phys, 190, 351, doi.org/10.1016/S0021-9991(03)00279-1 ; Ansumali (2002), Kinetic boundary conditions in the lattice Boltzmann method, Phys Rev, 66, 026311. ; Zou (1997), On pressure and velocity boundary conditions for the lattice Boltzmann BGK model, Phys Fluids, 9, 1591, doi.org/10.1063/1.869307 ; Higuera (1989), Boltzmann approach to lattice gas simulations, Europhys Lett, 9, 663, doi.org/10.1209/0295-5075/9/7/009 ; Allen (2016), Moment - based boundary conditions for lattice Boltzmann simulations of natural convection in cavities Fluid : An Int, Prog Dyn J, 16, 216. ; He (1997), Analytic solutions of simple flows and analysis of nonslip boundary conditions for the lattice Boltzmann BGK model, Stat Phys, 87. ; Noble (1995), A consistent hydrodynamic boundary condition for the lattice Boltzmann method, Phys Fluids, 7, 203, doi.org/10.1063/1.868767 ; Latt (2006), Lattice Boltzmann method with regularized pre - collision distribution functions, Comput Fluid, 72, 165. ; Qian (1992), Lattice BGK models for Navier - Stokes equation, Europhys Lett, 17, 479, doi.org/10.1209/0295-5075/17/6/001 ; He (1998), Discrete Boltzmann equation model for nonideal gases, Phys Rev, 13. ; Botella (1998), Benchmark spectral results on the lid - driven cavity flow, Comput Fluids, 27, 421, doi.org/10.1016/S0045-7930(98)00002-4 ; Bruneau (1990), An efficient scheme for solving steady incompressible Navier - Stokes equations, Comput Phys, 89, 389, doi.org/10.1016/0021-9991(90)90149-U ; Lallemand (2000), Theory of the lattice Boltzmann method : Dispersion dissipation isotropy Galilean invariance , and stability, Phys Rev, 61, 6546. ; He (1997), A priori derivation of the lattice Boltzmann equation, Phys Rev, 6333. ; Benzi (1990), Turbulence modelling by nonhydrodynamic variables, Europhys Lett, 13, 727, doi.org/10.1209/0295-5075/13/8/010 ; Ghia (1982), High - resolutions for incompressible flow using the Navier - Stokes equations and a multigrid method, Comput Phys, 48, 387, doi.org/10.1016/0021-9991(82)90058-4 ; Deng (1994), Incompressible flow calculations with a consistent physical interpolation finite volume approach, Comput Fluids, 23, 1029, doi.org/10.1016/0045-7930(94)90003-5 ; Shan (2006), Kinetic theory representation of hydrodynamics : a way beyond the Navier Stokes equation, Fluid Mech, 550. ; Mussa (2008), Numerical simulation of lid - driven cavity flow using the lattice Boltzmann method InWSEAS International Conference Mathematics and Computers in Science and Engineering, Proceedings. ; Reis (2012), Moment - based formulation of Navier Maxwell slip boundary conditions for lattice Boltzmann simulations of rarefied flows in microchannels, Phys Fluids, doi.org/10.1063/1.4764514 ; Sahin (2003), A novel fully implicit finite volume method applied to the lid - driven cavity problem part i : High Reynolds number flow calculations Fluids, Int J, 42. ; Luo (2011), al Numerics of the lattice boltzmann method : Effects of collision models on the lattice boltzmann simulations, Phys Rev, 056710.