Book Description
Lattice Boltzmann Method (LBM) has become a viable alternative to Navier-Stokes Direct Numerical Simulations (DNS) in fluid dynamics research. The key of this success is the accuracy/simplicity and parallelization compliant property of the stream-collision algorithm. One shortcoming however, comes from the limitation to spatially uniform cubic grids. To overcome this, several LBM extension to non-homogeneous grids have been proposed. These techniques have been reviewed in this thesis. Such review suggests that a better refinement technique should fulfill some properties: obey conservation laws and be stable. This suggests a pathway to adopt Finite Volume approaches (FV LBM). A review on such volumetric approach to LBM concludes that although interesting, at present such methods suffer from several drawbacks. In this study, a new FV discretization method for the Lattice Boltzmann equation that combines high accuracy with limited computational cost is presented. In order to assess the performance of the FV method we carry out a systematic comparison, focused on accuracy and computational performances, with the standard streaming (ST) Lattice Boltzmann equation algorithm. In particular we aim at clarifying whether and in which conditions the proposed algorithm, and more generally any FV algorithm, can be taken as the method of choice in fluid-dynamics LB simulations. We report the first successful simulation of high-Rayleigh number convective flow performed by a Lattice Boltzmann FV based algorithm with wall grid refinement.