Abstract
It is well known that the lattice Boltzmann equation method (LBE) can model the incompressible Navier-Stokes (NS) equations in the limit where density goes to a constant. In a LBE simulation, however, the density cannot be constant because pressure is equal to density times the square of sound speed, hence a compressibility error seems inevitable for the LBE to model incompressible flows. This work uses a modified equilibrium distribution and a modified velocity to construct an LBE which models time-independent (steady) incompressible flows with significantly reduced compressibility error. Computational results in 2D cavity flow and in a 2D flow with an exact solution are reported.
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References
D. O. Martinez, W. H. Matthaeus, S. Chen, and D. C. Montgomery,Phys. Fluids 6(3):1285 (1994).
S. Hou, Q. Zou, S. Chen, G. D. Doolen, and A. C. Cogley,J. Comput. Phys. 118:329 (1995).
M. B. Reider and J. D. Sterling, Accuracy of discrete-velocity BGK models for the simulation of the incompressible Navier-Stokes equations,Computers Fluids, to appear (1995).
B. H. Elton, Comparisons of lattice Boltzmann methods and a finite-difference method for a two-dimensional viscous Burgers equation, submitted.
Y. Qian, D. d'Humières, and P. Lallemand,Europhys. Lett. 17(6):479 (1992).
Y. Qian, Ph.D. thesis, Université Pierre et Marie Curie (January 1990).
J. D. Sterling and S. Chen, Stability analysis of the lattice Boltzmann method,J. Comput. Phys., to appear (1995).
P. A. Skordos,Phys. Rev. E 48:6 (1993).
U. Frisch, D. d'Humières, B. Hasslacher, P. Lallemand, Y. Pomeau, and J.-P. Rivet,Complex Systems 1:649 (1987).
D. d'Humières and P. Lallemand,Complex Systems 1:599 (1987).
L. P. Kadanoff, G. R. McNamara, and G. Zanetti,Complex Systems 1:791 (1987).
F. J. Alexander, H. Chen, S. Chen and G. D. Doolen,Phys. Rev. A 46:1967 (1992).
U. Ghia, K. N. Ghia, and C. Y. Shin,J. Comput. Phys. 48:387 (1982).
Y. H. Qian and S. A. Orszag,Europhys. Lett. 21(3):255 (1993).
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Zou, Q., Hou, S., Chen, S. et al. A improved incompressible lattice Boltzmann model for time-independent flows. J Stat Phys 81, 35–48 (1995). https://doi.org/10.1007/BF02179966
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DOI: https://doi.org/10.1007/BF02179966