Abstract
In this thesis, the lattice Boltzmann method is combined with the immersed boundary technique to simulate complex geometry flows both with stationary and moving boundaries. The complex geometry is represented by Lagrangian markers and forces are exerted at the Lagrangian markers in order to satisfy exactly the prescribed velocity of the boundary. This force at the Lagrangian markers is then distributed to the Eulerian grid by a well-chosen discretized delta function. With the known force field in the Eulerian grid to mimic the boundary, the lattice Boltzmann method is used to compute the flow field where the complex geometry is immersed inside the Cartesian computational domain. The proposed method is examined by computing decaying vortex flow, lid driven cavity flow, rotating cylinder flow and flows over both stationary and moving cylinder. All the numerical results agree reasonably well with the analytical solution or the benchmark solution, and the Galilean invariance is satisfied. The influences of the Lagrangian marker spacing on the solution accuracy are also examined. It was observed that the error on the Eulerian grid increases when reducing the Lagrangian marker spacing. The predicted results also show a discontinuous pressure field across the immersed boundary, a phenomenon to be clarified in future study.