Abstract
A hydrodynamic boundary condition is developed for lattice Boltzmann hydrodynamics using a square, orthogonal grid. A constraint based on energy considerations is developed to provide closure for the equations which govern the particle distribution at the boundaries. This boundary condition is applied to the two-dimensional, steady flow of an incompressible fluid behind a grid, known as Kovasznay flow. The results are compared to those using alternate boundary conditions using the known exact solution. The hydrodynamic boundary condition produces quadratic spatial convergence, while alternate techniques fail to maintain this second-order accuracy.
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References
U. Frisch, B. Hasslacher, and Y. Pomeau, Lattice-gas automata for the Navier-Stokes equation,Phys. Rev. Lett. 56:2505 (1986).
G. McNamara and G. Zanetti, Use of the Boltzmann equation to simulate lattice-gas automata,Phys. Rev. Lett. 61:2332 (1988).
F. Higuera and J. Jimenez, Lattice gas dynamics with enhanced collisions,Europhys. Lett. 9:663 (1989).
H. Chen, S. Chen, and W. H. Matthaeus, Recovery of the Navier-Stokes equations using a lattice Boltzmann method,Phys. Rev. A 45:R5339 (1991).
S. Y. Chen, H. D. Chen, D. Martinez, and W. Matthaeus, Lattice Boltzmann model for simulation of magnetohydrodynamics,Phys. Rev. Lett. 67:3776 (1991).
Y. H. Qian, D. d'Humières, and P. Lallemand, Lattice BGK models for the Navier-Stokes equation,Europhys. Lett. 17:479 (1992).
D. d'Humières and P. Lallemand, Numerical simulations of hydrodynamics with lattice gas automata in two dimensions,Complex Systems 1:599 (1987).
R. Cornubert, D. d'Humières, 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 France 4:191 (1994).
D. P. Ziegler, Boundary conditions for lattice Boltzmann simulations,J. Stat. Phys. 71:1171 (1993).
P. A. Skordos, Initial and boundary conditions for the lattice Boltzmann method,Phys. Rev. E 48:4823 (1993).
D. R. Noble, S. Chen, J. G. Georgiadis, and R. O. Buckius, A consistent hydrodynamic boundary condition for the lattice Boltzmann method,Phys. Fluids 7:203 (1995).
P. Bhatnagar, E. P. Gross, and M. K. Krook, A model for collision processes in gases. I. Small amplitude processes in charged and neutral one-component systems,Phys. Rev. 94:511 (1954).
F. J. Alexander, S. Chen, and J. D. Sterling, Lattice Boltzmann thermohydrodynamics,Phys. Rev. E 47:2249 (1993).
L. I. G. Kovasznay, Laminar flow behind a two-dimensional grid,Proc. Camb. Phil. Soc. 48 (1948).
Y. H. Qian and S. A. Orzag, Lattice BGK model for the Navier-Stokes equation: Nonlinear deviation in compressible regimes,Europhys. Lett. 21:255 (1993).
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Noble, D.R., Georgiadis, J.G. & Buckius, R.O. Direct assessment of lattice Boltzmann hydrodynamics and boundary conditions for recirculating flows. J Stat Phys 81, 17–33 (1995). https://doi.org/10.1007/BF02179965
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DOI: https://doi.org/10.1007/BF02179965