Abstract: The lattice Boltzmann method is a class of methods in computational fluid dynamics for simulating fluid flow. Implementations on unstructured grids are particularly relevant for various engineering applications, where geometric flexibility or high resolution near a body or a wall is required.

The main topic of this thesis is to further develop unstructured lattice Boltzmann methods for simulations of Newtonian fluid flow in three dimensions, in particular porous flow. Two methods are considered in this thesis based on the finite volume method and finite element method, respectively.
The formulation based on the finite volume method is developed for simulations of laminar single phase flow. The implementation is applied to a real sample of a porous rock and the permeability is numerically determined from the steady state flow field. Detailed analysis of the scheme reveals that the stability region depends on the method of time integration.
The formulation based on the finite element method exhibits improved stability and is therefore used for two applications. Firstly, together with a free-energy model two-phase flow is simulated at large density and kinematic viscosity contrasts including surface wettability. Benchmark problems quantify the accuracy of the method and the effects of two different finite element discretizations. Secondly, a direct numerical simulation of single phase turbulent flow is conducted in a square duct with wall imperfections. The imperfections are observed to break the symmetry of the corner vortices. Furthermore, the coherent structures of the flow are examined by decomposing the flow into a set of energetic modes using proper orthogonal decomposition. The transition between structures is characterized by the detachment of an old structure and the initiation of a new at the walls, which corroborates experimental measurements in cylindrical pipes.