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
doi:10.4208/cicp.151210.140711a

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.


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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: ahad.zarghami@gmail.com (A. Zarghami), mjmaghrebi@um.ac.ir (M. J. Maghrebi), j.ghasemi@znu.ac.ir (J. Ghasemi), Stefano.ubertini@uniparthenope.it (S. Ubertini)
 

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