A consistent hydrodynamic boundary condition for the lattice Boltzmann method

David R. Noble, Shiyi Chen, John G. Georgiadis, Richard O. Buckius

Research output: Contribution to journalArticle

Abstract

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.

Original languageEnglish (US)
Pages (from-to)203-209
Number of pages7
JournalPhysics of fluids
Volume7
Issue number1
DOIs
StatePublished - 1995

ASJC Scopus subject areas

  • Computational Mechanics
  • Condensed Matter Physics
  • Mechanics of Materials
  • Mechanical Engineering
  • Fluid Flow and Transfer Processes

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    Noble, D. R., Chen, S., Georgiadis, J. G., & Buckius, R. O. (1995). A consistent hydrodynamic boundary condition for the lattice Boltzmann method. Physics of fluids, 7(1), 203-209. https://doi.org/10.1063/1.868767