Abstract
In this thesis, three major issues are discussed. First, a consistent boundary condition for 2D and 3D lattice Boltzmann simulations is proposed. The unknown distribution functions are obtained from the known distribution functions and the correction factors, where the correction factors at the boundary nodes are evaluated directly from the de‾nitions of density and momentum. This boundary condition is applied to two-dimensional Poiseuille flow, Couette flow with wall injection, and three-dimensional square duct flow. Numerical simulation indicate that the formulation is second order accurate. Then, we focus on the flow including an immersed boundary. Two kinds of immersed boundary treatment are proposed. One is the combination of direct forcing approach in the immersed boundary method and the lattice Boltzmann method(Method A), another is the curved boundary treatment in the lattice Boltzmann method(Method B). Three flow problems are simulated utilizing our immersed boundary treatments, i.e. decaying vortex, flow over an asymmetrically placed cylinder in a channel, and in-line oscillating cylinder in a fluid at rest. The results show that both methods can model the velocity field well, but some inaccuracy of pressure occurs. This issue deserves further study.