A near-boundary modification for the link bounce-back boundary condition in the lattice Boltzmann method. (English) Zbl 1349.76723
Summary: The bounce-back boundary condition in the lattice Boltzmann method distorts curved or inclined boundaries by forcing them to conform to a rectangular grid. This paper proposes a modification that reduces the effect of this discretization on the fluid flow. The modification takes the form of the addition of a type of node that is neither solid nor fluid, called the “sticky node”. Sticky nodes are used in all cells that contain both fluid and solid. They are treated like fluid nodes with modified viscosity, body force, and velocity calculation. The method is applied to the LBGK model on a D2Q9 grid, and the accuracy of the method is evaluated using several test cases. Decreased discretization artifacts and decreased sensitivity to grid alignment are demonstrated, compared to the standard link bounce-back boundary condition. The method is computationally efficient, local, and demonstrates good numerical stability.
MSC:
| 76M28 | Particle methods and lattice-gas methods |
| 76D10 | Boundary-layer theory, separation and reattachment, higher-order effects |
References:
| [1] | Gunstensen, A. K.; Rothman, D. H.; Zaleski, S.; Zanetti, G., Lattice Boltzmann model of immiscible fluids, Phys. Rev. A, 43, 8, 4320 (1991) |
| [2] | Grunau, D.; Chen, S.; Eggert, K., A lattice Boltzmann model for multiphase fluid flows, Phys. Fluids A, Fluid Dyn. (1989-1993), 5, 10, 2557-2562 (1993) · Zbl 0797.76095 |
| [3] | Dawson, S. P.; Chen, S.; Doolen, G., Lattice Boltzmann computations for reaction-diffusion equations, J. Chem. Phys., 98, 2, 1514-1523 (1993) |
| [4] | Guo, Z.; Zhao, T., Lattice Boltzmann model for incompressible flows through porous media, Phys. Rev. E, 66, 3, Article 036304 pp. (2002) |
| [5] | Pan, C.; Luo, L.-S.; Miller, C. T., An evaluation of lattice Boltzmann schemes for porous medium flow simulation, Comput. Fluids, 35, 8, 898-909 (2006) · Zbl 1177.76323 |
| [6] | Pomeau, B. H.Y.; Frisch, U., Lattice-gas automata for the Navier-Stokes equation, Phys. Rev. Lett., 56, 14, 1505 (1986) |
| [7] | Chen, S.; Doolen, G. D., Lattice Boltzmann method for fluid flows, Annu. Rev. Fluid Mech., 30, 1, 329-364 (1998) · Zbl 1398.76180 |
| [8] | He, X.; Luo, L.-S., A priori derivation of the lattice Boltzmann equation, Phys. Rev. E, 55, 6, Article R6333 pp. (1997) |
| [9] | Abe, T., Derivation of the lattice Boltzmann method by means of the discrete ordinate method for the Boltzmann equation, J. Comput. Phys., 131, 1, 241-246 (1997) · Zbl 0877.76062 |
| [10] | Qian, Y.; d’Humières, D.; Lallemand, P., Lattice BGK models for Navier-Stokes equation, Europhys. Lett., 17, 6, 479 (1992) · Zbl 1116.76419 |
| [11] | Chen, H.; Chen, S.; Matthaeus, W. H., Recovery of the Navier-Stokes equations using a lattice-gas Boltzmann method, Phys. Rev. A, 45, 8, Article R5339 pp. (1992) |
| [12] | Succi, S.; d’Humières, D.; Qian, Y.; Orszag, S., On the small-scale dynamical behavior of lattice BGK and lattice Boltzmann schemes, J. Sci. Comput., 8, 3, 219-230 (1993) · Zbl 0783.76005 |
| [13] | Guo, Z.; Shi, B.; Wang, N., Lattice BGK model for incompressible Navier-Stokes equation, J. Comput. Phys., 165, 1, 288-306 (2000) · Zbl 0979.76069 |
| [14] | Lammers, P.; Beronov, K.; Volkert, R.; Brenner, G.; Durst, F., Lattice BGK direct numerical simulation of fully developed turbulence in incompressible plane channel flow, Comput. Fluids, 35, 10, 1137-1153 (2006) · Zbl 1177.76160 |
| [15] | Gan, Y.; Xu, A.; Zhang, G.; Yang, Y., Lattice BGK kinetic model for high-speed compressible flows: hydrodynamic and nonequilibrium behaviors, Europhys. Lett., 103, 2, 24003 (2013) |
| [16] | Frisch, U.; d’Humiéres, D.; Hasslacher, B.; Lallemand, P.; Pomeau, Y.; Rivet, J.-P., Lattice gas hydrodynamics in two and three dimensions, Complex Syst., 1, 4, 649-707 (1987) · Zbl 0662.76101 |
| [17] | Cornubert, R.; d’Humières, D.; Levermore, D., A Knudsen layer theory for lattice gases, Phys. D, Nonlinear Phenom., 47, 1, 241-259 (1991) · Zbl 0717.76100 |
| [18] | Ginzbourg, I.; Adler, P., Boundary flow condition analysis for the three-dimensional lattice Boltzmann model, J. Phys. II, 4, 2, 191-214 (1994) |
| [19] | He, X.; Zou, Q.; Luo, L.-S.; Dembo, M., Analytic solutions of simple flows and analysis of nonslip boundary conditions for the lattice Boltzmann BGK model, J. Stat. Phys., 87, 1-2, 115-136 (1997) · Zbl 0937.82043 |
| [20] | Ladd, A. J., Numerical simulations of particulate suspensions via a discretized Boltzmann equation. Part 1. Theoretical foundation, J. Fluid Mech., 271, 285-309 (1994) · Zbl 0815.76085 |
| [21] | Ziegler, D. P., Boundary conditions for lattice Boltzmann simulations, J. Stat. Phys., 71, 5-6, 1171-1177 (1993) · Zbl 0943.82552 |
| [22] | Noble, D. R.; Chen, S.; Georgiadis, J. G.; Buckius, R. O., A consistent hydrodynamic boundary condition for the lattice Boltzmann method, Phys. Fluids (1994-present), 7, 1, 203-209 (1995) · Zbl 0846.76086 |
| [23] | Inamuro, T.; Yoshino, M.; Ogino, F., A non-slip boundary condition for lattice Boltzmann simulations, Phys. Fluids (1994-present), 7, 12, 2928-2930 (1995) · Zbl 1027.76631 |
| [24] | Skordos, P., Initial and boundary conditions for the lattice Boltzmann method, Phys. Rev. E, 48, 6, 4823 (1993) |
| [25] | Latt, J., Hydrodynamic limit of lattice Boltzmann equations (2007), University of Geneva, Ph.D. thesis |
| [26] | Chen, S.; Martinez, D.; Mei, R., On boundary conditions in lattice Boltzmann methods, Phys. Fluids (1994-present), 8, 9, 2527-2536 (1996) · Zbl 1027.76630 |
| [27] | Latt, J.; Chopard, B.; Malaspinas, O.; Deville, M.; Michler, A., Straight velocity boundaries in the lattice Boltzmann method, Phys. Rev. E, 77, 5, Article 056703 pp. (2008) |
| [28] | Noble, D.; Torczynski, J., A lattice-Boltzmann method for partially saturated computational cells, Int. J. Mod. Phys. C, 9, 08, 1189-1201 (1998) |
| [29] | Verberg, R.; Ladd, A., Lattice-Boltzmann model with sub-grid-scale boundary conditions, Phys. Rev. Lett., 84, 10, 2148 (2000) |
| [30] | Verberg, R.; Ladd, A., Accuracy and stability of a lattice-Boltzmann model with subgrid scale boundary conditions, Phys. Rev. E, 65, 1, Article 016701 pp. (2001) · Zbl 1046.76037 |
| [31] | Filippova, O.; Hänel, D., Grid refinement for lattice-BGK models, J. Comput. Phys., 147, 1, 219-228 (1998) · Zbl 0917.76061 |
| [32] | Mei, R.; Luo, L.-S.; Shyy, W., An accurate curved boundary treatment in the lattice Boltzmann method, J. Comput. Phys., 155, 2, 307-330 (1999) · Zbl 0960.82028 |
| [33] | Yu, D.; Mei, R.; Shyy, W., A unified boundary treatment in lattice Boltzmann method, 2003 (2003), AIAA 2003-953, New York |
| [34] | Bao, J.; Yuan, P.; Schaefer, L., A mass conserving boundary condition for the lattice Boltzmann equation method, J. Comput. Phys., 227, 18, 8472-8487 (2008) · Zbl 1143.82319 |
| [35] | Bouzidi, M.; Firdaouss, M.; Lallemand, P., Momentum transfer of a Boltzmann-lattice fluid with boundaries, Phys. Fluids (1994-present), 13, 11, 3452-3459 (2001) · Zbl 1184.76068 |
| [36] | Yin, X.; Zhang, J., An improved bounce-back scheme for complex boundary conditions in lattice Boltzmann method, J. Comput. Phys., 231, 11, 4295-4303 (2012) · Zbl 1426.76622 |
| [37] | Bhatnagar, P. L.; Gross, E. P.; Krook, M., A model for collision processes in gases. I. Small amplitude processes in charged and neutral one-component systems, Phys. Rev., 94, 3, 511 (1954) · Zbl 0055.23609 |
| [38] | Zou, Q.; He, X., On pressure and velocity boundary conditions for the lattice Boltzmann BGK model, Phys. Fluids (1994-present), 9, 6, 1591-1598 (1997) · Zbl 1185.76873 |
| [39] | Sangani, A.; Acrivos, A., Slow flow past periodic arrays of cylinders with application to heat transfer, Int. J. Multiph. Flow, 8, 3, 193-206 (1982) · Zbl 0487.76048 |
| [40] | Fornberg, B., Steady incompressible flow past a row of circular cylinders, J. Fluid Mech., 225, 655-671 (1991) · Zbl 0722.76023 |
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