A consistent hydrodynamic boundary condition for the lattice Boltzmann method

Journal Article · Sun Jan 01 04:00:00 EST 1995 · Physics of Fluids; (United States)

DOI:https://doi.org/10.1063/1.868767· OSTI ID:7065269

Noble, D R ^[1]; Chen, S ^[2]; Georgiadis, J G ^[1]; Buckius, R O ^[1]

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1. Department of Mechanical and Industrial Engineering, University of Illinois, Urbana, Illinois 61801 (United States)
2. Center for Nonlinear Studies and Theoretical Division, Los Alamos National Laboratory, Los Alamos, New Mexico 87545 (United States)

A hydrodynamic boundary condition is developed to replace the heuristic bounce-back boundary condition used in the majority of lattice Boltzmann simulations. This boundary condition is applied to the two-dimensional, steady flow of an incompressible fluid between two parallel plates. Poiseuille flow with stationary plates, and a constant pressure gradient is simulated to machine accuracy over the full range of relaxation times and pressure gradients. A second problem involves a moving upper plate and the injection of fluid normal to the plates. The bounce-back boundary condition is shown to be an inferior approach for simulating stationary walls, because it actually mimics boundaries that move with a speed that depends on the relaxation time. When using accurate hydrodynamic boundary conditions, the lattice Boltzmann method is shown to exhibit second-order accuracy.

• OSTI ID: 7065269
• Journal Information: Physics of Fluids; (United States), Journal Name: Physics of Fluids; (United States) Vol. 7:1; ISSN 1070-6631; ISSN PHFLE6
• Country of Publication: United States
• Language: English

Related Subjects

661300* -- Other Aspects of Physical Science-- (1992-)
71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
BOLTZMANN EQUATION
BOUNDARY CONDITIONS
BOUNDARY-VALUE PROBLEMS
DIFFERENTIAL EQUATIONS
DIRICHLET PROBLEM
DISTRIBUTION FUNCTIONS
EQUATIONS
FLUID FLOW
FLUID MECHANICS
FUNCTIONS
HYDRODYNAMICS
INCOMPRESSIBLE FLOW
MECHANICS
PARTIAL DIFFERENTIAL EQUATIONS
STEADY FLOW
VISCOUS FLOW