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Physics of Fluids / Volume 9 / Issue 6

Phys. Fluids 9, 1591 (1997); http://dx.doi.org/10.1063/1.869307 (8 pages)

On pressure and velocity boundary conditions for the lattice Boltzmann BGK model

Qisu Zou1,2 and Xiaoyi He3

1Theoretical Division, Los Alamos National Lab, Los Alamos, New Mexico 87545
2Department of Mathematics, Kansas State University, Manhattan, Kansas 66506
3Center for Nonlinear Studies and Theoretical Biology and Biophysics Group, Los Alamos National Laboratory, Los Alamos, New Mexico 87545

(Received 10 August 1995; accepted 24 February 1997)

Pressure (density) and velocity boundary conditions are studied for 2-D and 3-D lattice Boltzmann BGK models (LBGK) and a new method to specify these conditions is proposed. These conditions are constructed in consistency with the wall boundary condition, based on the idea of bounceback of the non-equilibrium distribution. When these conditions are used together with the incompressible LBGK model [J. Stat. Phys. 81, 35 (1995)] the simulation results recover the analytical solution of the plane Poiseuille flow driven by a pressure (density) difference. The half-way wall bounceback boundary condition is also used with the pressure (density) inlet/outlet conditions proposed in this paper and in Phys. Fluids 8, 2527 (1996) to study 2-D Poiseuille flow and 3-D square duct flow. The numerical results are approximately second-order accurate. The magnitude of the error of the half-way wall bounceback boundary condition is comparable with that of other published boundary conditions and it has better stability behavior. © 1997 American Institute of Physics.

© 1997 American Institute of Physics

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KEYWORDS and PACS

Keywords

Poiseuille flow, flow simulation, pipe flow, nonequilibrium flow, BOLTZMANN EQUATION, PRESSURE DEPENDENCE, VELOCITY, BOUNDARY CONDITIONS, EQUILIBRIUM, DISTRIBUTION, SIMULATION, ANALYTICAL SOLUTION, DENSITY, STABILITY, INCOMPRESSIBLE FLOW

PACS

  • 47.60.-i

    Flow phenomena in quasi-one-dimensional systems

  • 47.11.-j

    Computational methods in fluid dynamics

  • 47.70.Nd

    Nonequilibrium gas dynamics

ARTICLE DATA

Digital Object Identifier
http://dx.doi.org/10.1063/1.869307

PUBLICATION DATA

ISSN

1070-6631 (print)  
1089-7666 (online)

Publisher

$abstract.society.value is a Member of CrossRef American Institute of Physics

For access to fully linked references, you need to log in.
    S. Succi, D. d'Humières, Y. Qian, and S. A. Orszag, "On the small-scale dynamical behavior of lattice BGK and lattice Boltzmann schemes," J. Sci. Comput. 8, 219 (1993PHFLE6000008000009002527000001).

    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 (1995PHFLE6000007000001000203000001).

    P. A. Skordos, "Initial and boundary conditions for the lattice Boltzmann method," Phys. Rev. E 48, 4823 (1993).

    T. Inamuro, M. Yoshino, and F. Ogino, "A non-slip boundary condition for lattice Boltzmann simulations," Phys. Fluids 7, 2928 (1996PHFLE6000007000012002928000001).

    R. S. Maier, R. S. Bernard, and D. W. Grunau, "Boundary conditions for the lattice Boltzmann method," Phys. Fluids 8, 1788 (1996PHFLE6000008000007001788000001).

    S. Chen, D. O. Martinez, and R. Mei, "On boundary conditions in lattice Boltzmann methods," Phys. Fluids 8, 2527 (1996PHFLE6000008000009002527000001).

    S. Chen, H. Chen, D. O. Martinez, and W. H. Matthaeus, "Lattice Boltzmann model for simulation of magnetohydrodynamics," Phys. Rev. Lett. 67, 3776 (1991).

    H. Chen, S, Chen, and W. H. Matthaeus, "Recovery of Navier-Stokes equations using a lattice-gas Boltzmann method," Phys. Rev. A 45, 5771 (1992).


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