Lattice-Boltzmann Methods with Hierarchically Refined Meshes

Since its initiation in the late 1980s, the lattice-Boltzmann method (LBM) has emerged as an eminent tool for numerical investigations of fluid flows involving complex physics and highly intricate geometries. Compared to conventional approaches, which utilize a discretization of the Navier-Stokes equations, the LB method offers a simple algorithmic structure, very good parallel scale-up, and an efficient boundary treatment for fixed walls. However, the method is still subject to ongoing research and development concerning its complex stability behavior and the use of non-uniform meshes.The purpose of this work is to explore possible improvements and new applications for LBM by developing a highly productive parallel LB flow solver based on hierarchically refined Cartesian meshes. The numerical method and the developed techniques for local grid refinement, solution-adaptation, and large-eddy simulations (LES) are described in detail. To validate the implemented methods, two-dimensional and threedimensional laminar and turbulent flows over blunt bodies at Reynolds numbers up to ReD = 3700 are simulated and adaptive mesh refinement is successfully applied in simulations of steady and unsteady cylinder flow. The results evidence a very good agreement with reference values from the literature regarding the velocity field, the wall-pressure distribution, and the coefficients for drag, lift and vortex-shedding frequency. Additionally, the LBM is successfully applied for a direct numerical simulation (DNS) and a LES study of a temporally evolving shear layer. It is shown that the LES approach delivers reliable results for turbulent flows proving the applicability of LBM for practical engineering applications. In an additional investigation, the classical Bhatnagar-Gross-Krook (BGK) collision operator is compared to moment-based methods in studies of laminar and turbulent wall-bounded flows with respect to stability and accuracy. All methods are found to deliver consistent results, whereas the LBGK method shows a higher susceptibility to pressure oscillations.In the last part of this work, the developed methods are applied for simulations of the flow in a realistic model of the human lung. Time-resolved simulations of oscillating lung flow are compared with experimental data from particle-image velocimetry (PIV) measurements and evidence a good agreement of the overall flow structure. In a next step, the unsteady three-dimensional flow field is analyzed in detail by which fundamental insight to highly intricate respiratory flow mechanisms is gained. From the findings of this thesis, it is concluded that the LBM in combination with local grid refinement yields accurate results in multiple flow regimes and dramatically improves the computational efficiency. The presented techniques form the basis of a highly flexible LB framework and contribute to extending the field of applications of LBM towards complex engineering flow fields.