Shear stress in lattice Boltzmann simulations

Timm Krueger*, Fathollah Varnik, Dierk Raabe

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

Abstract

A thorough study of shear stress within the lattice Boltzmann method is provided. Via standard multiscale Chapman-Enskog expansion we investigate the dependence of the error in shear stress on grid resolution showing that the shear stress obtained by the lattice Boltzmann method is second-order accurate. This convergence, however, is usually spoiled by the boundary conditions. It is also investigated which value of the relaxation parameter minimizes the error. Furthermore, for simulations using velocity boundary conditions, an artificial mass increase is often observed. This is a consequence of the compressibility of the lattice Boltzmann fluid. We investigate this issue and derive an analytic expression for the time dependence of the fluid density in terms of the Reynolds number, Mach number, and a geometric factor for the case of a Poiseuille flow through a rectangular channel in three dimensions. Comparison of the analytic expression with results of lattice Boltzmann simulations shows excellent agreement.

Original languageEnglish
Article number046704
Number of pages14
JournalPhysical Review E - Statistical, Nonlinear and Soft Matter Physics
Volume79
Issue number4
DOIs
Publication statusPublished - Apr 2009

Keywords

  • channel flow
  • compressibility
  • compressible flow
  • convergence
  • flow simulation
  • laminar flow
  • lattice Boltzmann methods
  • Mach number
  • Poiseuille flow
  • shear flow
  • NAVIER-STOKES EQUATION
  • BOUNDARY-CONDITIONS
  • GAS AUTOMATA
  • FLUID-FLOWS
  • BGK MODELS
  • HYDRODYNAMICS

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