@Article{CiCP-12-42,
author = {A. Zarghami, M. J. Maghrebi, J. Ghasemi and S. Ubertini},
title = {Lattice Boltzmann Finite Volume Formulation with Improved Stability},
journal = {Communications in Computational Physics},
year = {2012},
volume = {12},
number = {1},
pages = {42--64},
abstract = {<p style="text-align: justify;">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 &quot;stream and collide&quot; 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.</p>},
issn = {1991-7120},
doi = {https://doi.org/10.4208/cicp.151210.140711a},
url = {http://global-sci.org/intro/article_detail/cicp/7283.html}
}