The Lattice Boltzmann Method (LBM) is an appealing framework to apply to unsteady, incompressible, low Reynolds number flow due to its simplicity and potential for massive parallelisation. The immersed boundary method is often used in conjunction with the LBM to simulate flow around curved, moving boundaries in the interior of the fluid domain. In the immersed boundary method, the boundary is imposed on a non-conforming grid by applying an external forcing at the boundary. The distribution of this external forcing is calculated based on interpolation of nearby fluid nodes, and the force field is then distributed over a number of nearby fluid nodes.

The immersed interface method is an approach similar to the immersed boundary method, but imposes this applied force field directly on the solution field through jump conditions. It has yet to be correctly applied to the LBM framework. In this thesis, a proposal of an immersed interface method in the LBM is made, and its implementation is validated and compared against the immersed boundary method. To aid in this, a solver capable of solving fluid-structure interaction is developed.

It is shown that the immersed interface method in the LBM has significant benefits compared to the immersed boundary method, in particular with regards to reducing numerical oscillations in the spatial variation of the boundary force distribution, as well appearing to yield a slight increase in overall accuracy at the same level of grid refinement.