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Lattice Boltzmann Finite Volume Formulation with Improved Stability

Published online by Cambridge University Press:  20 August 2015

A. Zarghami ,
M. J. Maghrebi ,
J. Ghasemi  and
S. Ubertini
A. Zarghami*
Affiliation:
Department of Mechanical Engineering, Shahrood University of Technology, Shahrood, Iran
M. J. Maghrebi*
Affiliation:
Department of Mechanical Engineering, Ferdowsi University ofMashhad, Mashhad, Iran
J. Ghasemi*
Affiliation:
Faculty of Engineering, Zanjan University, Zanjan, Iran
S. Ubertini*
Affiliation:
Department of Technologies, University of Naples “Parthenope”, Naples, Italy
*
Corresponding author.Email:[email protected]
Email:[email protected]
Email:[email protected]
Email:[email protected]
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Abstract

The most severe limitation of the standard Lattice Boltzmann Method is the use of uniform Cartesian grids especially when there is a need for high resolutions near the body or the walls. Among the recent advances in lattice Boltzmann research to handle complex geometries, a particularly remarkable option is represented by changing the solution procedure from the original “stream and collide” to a finite volume technique. However, most of the presented schemes have stability problems. This paper presents a stable and accurate finite-volume lattice Boltzmann formulation based on a cell-centred scheme. To enhance stability, upwind second order pressure biasing factors are used as flux correctors on a D2Q9 lattice. The resulting model has been tested against a uniform flow past a cylinder and typical free shear flow problems at low and moderate Reynolds numbers: boundary layer, mixing layer and plane jet flows. The numerical results show a very good accuracy and agreement with the exact solution of the Navier-Stokes equation and previous numerical results and/or experimental data. Results in self-similar coordinates are also investigated and show that the time-averaged statistics for velocity and vorticity express self-similarity at low Reynolds numbers. Furthermore, the scheme is applied to simulate the flow around circular cylinder and the Reynolds number range is chosen in such a way that the flow is time dependent. The agreement of the numerical results with previous results is satisfactory.

Keywords

47.20.Ky47.11.DfLattice Boltzmann equationfinite volumestabilitycell-centered schemefree shear flows
Type
Research Article
Information
Communications in Computational Physics , Volume 12 , Issue 1 , July 2012 , pp. 42 - 64
Copyright
Copyright © Global Science Press Limited 2012

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