Commun. Comput. Phys., 12 (2012), pp. 42-64.

Lattice Boltzmann Finite Volume Formulation with Improved Stability

A. Zarghami 1*, M. J. Maghrebi 2, J. Ghasemi 3, S. Ubertini 4

1 Department of Mechanical Engineering, Shahrood University of Technology, Shahrood, Iran.
2 Department of Mechanical Engineering, Ferdowsi University of Mashhad, Mashhad, Iran.
3 Faculty of Engineering, Zanjan University, Zanjan, Iran.
4 Department of Technologies, University of Naples "Parthenope", Naples, Italy.

Received 15 December 2010; Accepted (in revised version) 14 July 2011
Available online 16 January 2012


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.

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PACS: 47.20.Ky, 47.11.Df
Key words: Lattice Boltzmann equation, finite volume, stability, cell-centered scheme, free shear flows.

*Corresponding author.
Email: (A. Zarghami), (M. J. Maghrebi), (J. Ghasemi), (S. Ubertini)

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