Using the Lid-Driven Cavity Flow to Validate Moment-Based Boundary Conditions for the Lattice Boltzmann Equation

• Autorzy: Mohammed S. , Reis T.

Identyfikatory

DOI

10.1515/meceng-2017-0004

• Języki publikacji: EN

Abstrakty

EN

The accuracy of the Moment Method for imposing no-slip boundary conditions in the lattice Boltzmann algorithm is investigated numerically using lid-driven cavity flow. Boundary conditions are imposed directly upon the hydrodynamic moments of the lattice Boltzmann equations, rather than the distribution functions, to ensure the constraints are satisfied precisely at grid points. Both single and multiple relaxation time models are applied. The results are in excellent agreement with data obtained from state-of-the-art numerical methods and are shown to converge with second order accuracy in grid spacing.

Słowa kluczowe

EN

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

PL

siatkowe równanie Boltzmanna; warunki brzegowe w odniesieniu do momentu; wielorelaksacyjne modele zderzeń w gazie sieciowym Boltzmanna; MRT

• Wydawca: Komitet Budowy Maszyn PAN
• Czasopismo: Archive of Mechanical Engineering
• Rocznik: 2017
• Tom: Vol. LXIV, nr 1
• Strony: 57--74
• Opis fizyczny: Bibliogr. 34 poz., rys., tab.

Twórcy

autor

Mohammed S.

• School of Computing Electronics and Mathematics, Plymouth University, PL4 8AA, UK

autor

Reis T.

• Department of Mathematical Sciences, University of Greenwich, SE10 9LS, UK

Bibliografia

• [1] F. Higuera and J. Jimenez. Boltzmann approach to lattice gas simulations. Europhys. Lett., 9:663, 1989.
• [2] YH. Qian, D. d’Humières, and P. Lallemand. Lattice BGK models for Navier-Stokes equation. Europhys. Lett., 17:479, 1992.
• [3] X. Shan, X.F. Yuan, and H. Chen. Kinetic theory representation of hydrodynamics: a way beyond the Navier–Stokes equation. J. Fluid Mech., 550:413–441, 2006.
• [4] X. He and L.S. Luo. A priori derivation of the lattice Boltzmann equation. Phys. Rev. E, 55:R6333, 1997.
• [5] D. d’Humieress. Generalized lattice-Boltzmann equations. Prog. Astronaut. Aeronaut., pages 450–458, 1992.
• [6] P. Lallemand and L.S. Luo. Theory of the lattice Boltzmann method: Dispersion, dissipation, isotropy, Galilean invariance, and stability. Phys. Rev. E, 61:6546, 2000.
• [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.
• [9] Z. Guo and C. Shu. Lattice Boltzmann method and its applications in engineering. World Scientific, 2013.
• [10] X.Y. He, Q.S. Zou, L.S. Luo, and M. Dembo. Analytic solutions of simple flows and analysis of nonslip boundary conditions for the lattice Boltzmann BGK model. J. Stat. Phys., 87:115–136, 1997.
• [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.
• [13] R. Gatignol. Kinetic theory boundary conditions for discrete velocity gases. Phys. Fluids (1958-1988), 20:2022–2030, 1977.
• [14] S. Ansumali and I. V Karlin. Kinetic boundary conditions in the lattice Boltzmann method. Phys. Rev. E, 66:026311, 2002.
• [15] Q. Zou and X. He. On pressure and velocity boundary conditions for the lattice Boltzmann BGK model. Phys. Fluids., 9:1591–1598, 1997.
• [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. Int. 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.
• [32] C.H. Bruneau and C. Jouron. An efficient scheme for solving steady incompressible Navier-Stokes equations. J. Comput. Phys., 89:389–413, 1990.
• [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.
• [34] G. Deng, J. Piquet, P. Queutey, and M. Visonneau. Incompressible flow calculations with a consistent physical interpolation finite volume approach. Comput. Fluids, 23:1029–1047, 1994.

Uwagi

PL

Opracowanie ze środków MNiSW w ramach umowy 812/P-DUN/2016 na działalność upowszechniającą naukę (zadania 2017).