Straight velocity boundaries in the lattice Boltzmann method

Jonas Latt, Bastien Chopard, Orestis Malaspinas, Michel Deville, and Andreas Michler
Phys. Rev. E 77, 056703 – Published 13 May 2008

Abstract

Various ways of implementing boundary conditions for the numerical solution of the Navier-Stokes equations by a lattice Boltzmann method are discussed. Five commonly adopted approaches are reviewed, analyzed, and compared, including local and nonlocal methods. The discussion is restricted to velocity Dirichlet boundary conditions, and to straight on-lattice boundaries which are aligned with the horizontal and vertical lattice directions. The boundary conditions are first inspected analytically by applying systematically the results of a multiscale analysis to boundary nodes. This procedure makes it possible to compare boundary conditions on an equal footing, although they were originally derived from very different principles. It is concluded that all five boundary conditions exhibit second-order accuracy, consistent with the accuracy of the lattice Boltzmann method. The five methods are then compared numerically for accuracy and stability through benchmarks of two-dimensional and three-dimensional flows. None of the methods is found to be throughout superior to the others. Instead, the choice of a best boundary condition depends on the flow geometry, and on the desired trade-off between accuracy and stability. From the findings of the benchmarks, the boundary conditions can be classified into two major groups. The first group comprehends boundary conditions that preserve the information streaming from the bulk into boundary nodes and complete the missing information through closure relations. Boundary conditions in this group are found to be exceptionally accurate at low Reynolds number. Boundary conditions of the second group replace all variables on boundary nodes by new values. They exhibit generally much better numerical stability and are therefore dedicated for use in high Reynolds number flows.

  • Figure
  • Figure
  • Figure
  • Figure
  • Figure
  • Figure
  • Figure
1 More
  • Received 5 January 2008

DOI:https://doi.org/10.1103/PhysRevE.77.056703

©2008 American Physical Society

Authors & Affiliations

Jonas Latt* and Bastien Chopard

  • University of Geneva, Geneva, Switzerland

Orestis Malaspinas, Michel Deville, and Andreas Michler

  • Ecole Polytechnique Fédérale de Lausanne, Lausanne, Switzerland

  • *Current address: Mathematics Department, Tufts University.
  • bastien.chopard@cui.unige.ch
  • Current address: Institute of Aerodynamics and Flow Technology, German Aerospace Center, Braunschweig, Germany.

Article Text (Subscription Required)

Click to Expand

References (Subscription Required)

Click to Expand
Issue

Vol. 77, Iss. 5 — May 2008

Reuse & Permissions
Access Options
Author publication services for translation and copyediting assistance advertisement

Authorization Required


×
×

Images

×

Sign up to receive regular email alerts from Physical Review E

Log In

Cancel
×

Search


Article Lookup

Paste a citation or DOI

Enter a citation
×