Abstract
The focus of the present thesis is to develop an immersed boundary based scheme to model 3-D complex geometry flows within the lattice Boltzmann method framework. Two key issues are addressed. Firstly is the numerical accuracy of the lattice Boltzmann models, and secondly is the capability of the immersed boundary concept to model complex flows. Here, 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 computational accuracy and efficiency of the immersed boundary based lattice Boltzmann method are examined by computing 3-D flows: (1) Fully developed flows in a square duct, (2) 3-D lid-driven cavity flow, (3) Flow over an asymmetrically placed cylinder in a square duct. (4) Parallel Computation of 3-D lid-driven cavity flow. Reasonable agreements with the analytical solution or the benchmark solution are obtained, though the present scheme is shown to be first order accurate.