Lattice Boltzmann Finite Volume Formulation with Improved Stability (Communications in Computational Physics, 2012)
The most severe limitation of the standard Lattice Boltzmann Method is theuse of uniform Cartesian grids especially when there is a need for high resolutions nearthe body or the walls. Among the recent advances in lattice Boltzmann research to handle complex geometries, a particularly remarkable option is represented by changingthe solution procedure from the original "stream and collide" to a finite volume technique. However, most of the presented schemes have stability problems. This paperpresents a stable and accurate finite-volume lattice Boltzmann formulation based on acell-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 testedagainst a uniform flow past a cylinder and typical free shear flow problems at low andmoderate Reynolds numbers: boundary layer, mixing layer and plane jet flows. Thenumerical results show a very good accuracy and agreement with the exact solutionof the Navier-Stokes equation and previous numerical results and/or experimentaldata. Results in self-similar coordinates are also investigated and show that the time-averaged statistics for velocity and vorticity express self-similarity at low Reynoldsnumbers. Furthermore, the scheme is applied to simulate the flow around circularcylinder and the Reynolds number range is chosen in such a way that the flow is timedependent. The agreement of the numerical results with previous results is satisfactory.