On boundary conditions in lattice Boltzmann methods

Physics of Fluids

Volumn 8, Issue 9, 1996, Pages 2527-2536

  Chen, Shiyi ^a,b   Martínez, Daniel ^a,b   Mei, Renwei ^c  

^a IBM T J WATSON RESEARCH CENTER   (United States)

^b LOS ALAMOS NATIONAL LABORATORY   (United States)

^c UNIVERSITY OF FLORIDA   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

BOUNDARY CONDITIONS; COUETTE FLOW; POISEUILLE FLOW;

EID: 0030476055     PISSN: 10706631     EISSN: None     Source Type: Journal    
DOI: 10.1063/1.869035     Document Type: Article

References (31)

1. U. Frisch, D. d'Humieres, B. Hasslacher, P. Lallemand, Y. Pomeau, and J.-P. Rivet, "Lattice gas hydrodynamics in two and three dimensions," Complex Syst. 1, 649 (1987).
2. D. O. Martínez, W. H. Matthacus, S. Chen and D. C. Montgomery, "Comparsion of spectral method and lattice Boltzmann simulations of two-dimensional hydrodynamics," Phys. Fluids 6, 1285 (1994).
3. A. Majda, Compressible Fluid Flow and Systems of Conservation Laws in Several Space Variables (Springer, New York, 1984).
4. M. B. Reider and J. D. Sterling, "Accuracy of discrete-velocity BGK models for the simulation of the incompressible Navier-Stokes equations," Comput. Fluids 24, 459 (1994).
5. R. Cornubert, D. d'Humieres, and D. Levermore, "A Knudsen layer theory for lattice gases," Physica D 47, 241 (1991); I. Ginzbourg and P. M. Adler, "Boundary flow condition analysis for the three-dimensional lattice Boltzmann model," J. Phys. II 4, 191 (1994).
6. R. Cornubert, D. d'Humieres, and D. Levermore, "A Knudsen layer theory for lattice gases," Physica D 47, 241 (1991); I. Ginzbourg and P. M. Adler, "Boundary flow condition analysis for the three-dimensional lattice Boltzmann model," J. Phys. II 4, 191 (1994).
7. D. R. Noble, S. Chen, J. G. Georgiadis, and R. O. Buckius, "A consistent hydrodynamics boundary condition for the lattice Boltzmann method," Phys. Fluids 7, 206 (1995).
8. R. S. Maier, R. S Bernard, and D. W. Grunau, "Boundary condtions for the lattice Boltzmann method," Los Alamos preprint (1995).
9. X. He and Q. Zou, "Analysis and boundary conditions of the lattice Boltzmann BGK model with two velocity compnents," Los Alamos preprint, LA-UR-95-2293.
10. T. Inamuro, M. Yoshino, and F. Ogino, "A non-slip boundary condition for lattice Boltzmann simulation," to appear in Phys. Fluids.
11. N. S. Martys and H. Chen, "Simulation of multicomponent fluids in complex three-dimensional geometries by the lattice Boltzmann method," Phys. Rev. E 53, 743 (1995).
12. S. Chen, H. Chen, D. O. Martínez, and W. H. Matthaeus, "Lattice Boltzmann model for simulation of magnetohydrodynamics," Phys. Rev. Lett. 67, 3776 (1991).
13. H. Chen, S. Chen, and W. H. Matthaeus, "Recovery of the Navier-Stokes equations using a lattice-gas Boltzmann method," Phys. Rev A 45, 5339 (1992).
14. Y. H. Qian, D. d'Humieres, and P. Lallemand, "Lattice BGK models for Navier-Stokes equation," Europhys. Lett. 17, 479 (1992).
15. J. D. Sterling and S. Chen, "Stability analysis of lattice Boltzmann methods," J. Comput. Phys. 123, 196 (1996).
16. S. Chen, Z. Wang, G. D. Doolen, and X. Shan, "Lattice Boltzmann computational fluid dynamics in three dimensions," J. Stat. Phys. 68, 379 (1992).
17. S. Hou, Q. Zou, S. Chen, G. D. Doolen, and A. C. Cogley, "Lattice Boltzmann simulation for laminar flow in three-dimensional cavity," submined to J. Comput. Phys. (1995).
18. A. K. Gunstensen, D. H. Rothman, and S. Zaleski, "Lattice Boltzmann model of immiscible fluids," Phys. Rev. A 43, 4320 (1991); D. Grunau, S. Chen, and K. Eggert, "A lattice Boltzmann model for multi-phase fluid flows," Phys. Fluids A 5, 2557 (1993); X. Shan and H. Chen, "Lattice Boltzmann model for simulating flows with multiple phases and components," Phys. Rev. E 47, 1815 (1993).
19. A. K. Gunstensen, D. H. Rothman, and S. Zaleski, "Lattice Boltzmann model of immiscible fluids," Phys. Rev. A 43, 4320 (1991); D. Grunau, S. Chen, and K. Eggert, "A lattice Boltzmann model for multi-phase fluid flows," Phys. Fluids A 5, 2557 (1993); X. Shan and H. Chen, "Lattice Boltzmann model for simulating flows with multiple phases and components," Phys. Rev. E 47, 1815 (1993).
20. A. K. Gunstensen, D. H. Rothman, and S. Zaleski, "Lattice Boltzmann model of immiscible fluids," Phys. Rev. A 43, 4320 (1991); D. Grunau, S. Chen, and K. Eggert, "A lattice Boltzmann model for multi-phase fluid flows," Phys. Fluids A 5, 2557 (1993); X. Shan and H. Chen, "Lattice Boltzmann model for simulating flows with multiple phases and components," Phys. Rev. E 47, 1815 (1993).
21. A. J. C. Ladd, "Numerical simulation of particulate suspensions via a discretized Boltzmann equation. Pan I. theoretical foundation," J. Fluid Mech. 271, 285 (1994).
22. A. J. J. Chorin, "A numerical method for solving incompressible viscous flow problems," J. Comput. Phys. 2, 12 (1967).
23. S. Hou, Q. Zou, S. Chen, G. Doolen, and A. C. Cogley, "Simulation of cavity flow by the lattice Boltzmann method," J. Comput. Phys. 118, 329 (1995).
24. L. Luo, "Lattice gas automata and lattice Boltzmann equations for two-dimensional hydrodynamics," Ph.D. thesis, Georgia Institute of Technology, 1993.
25. G. McNamara and B. Adler, in Microscopic Simulations of Complex Hydrodynamics Phenomena, edited by M. Mareschal and B. L. Holian (Plenum. New York. 1992).
26. D. P. Ziegler, "Boundary conditions for lattice Boltzmann simulations," J. Stat. Phys. 71, 1171 (1993).
27. R. Peyret and T. Taylor. Computational Methods for Fluid Flow (Springer, New York, 1983).
28. S. Pai. Viscous Flow Theory I-laminar Flow (Van Nostrandt, New York, 1956).
29. R. Mei and A. Plotkin, "A finite difference scheme for the solution of the steady Navier-Stokes equation," Comput. Fluids 14, 239 (1986); R. Mei, J. Xiong, and R. Tran-Son-Tay, "Motion of a sphere oscillating at low Reynolds numbers in a viscoelastic fluid filled cylindrical tube," submitted to J. Non-Newtonian Fluid Mech. (1995).
30. R. Mei and A. Plotkin, "A finite difference scheme for the solution of the steady Navier-Stokes equation," Comput. Fluids 14, 239 (1986); R. Mei, J. Xiong, and R. Tran-Son-Tay, "Motion of a sphere oscillating at low Reynolds numbers in a viscoelastic fluid filled cylindrical tube," submitted to J. Non-Newtonian Fluid Mech. (1995).
31. B. Fornberg, "Steady incompressible flow past a row of cylinders," J. Fluid Mech. 225, 655 (1991).