Abstract
In this thesis, we introduce the fundamental concepts of the immersed boundary method and also apply it to the simulation of two-dimensional interfacial flows. The governing equations are written in a usual immersed boundary formulation where a mixture of Eulerian flow and Lagrangian interfacial variables are used, and the linkage between these two set of variables is provided by the Dirac delta function which is constructed under certain postulates. A new type of smooth delta functions is compared with the original ones. The incompressible viscous Navier-Stokes equations are solved by a semi-implicit second-order projection method, and the interface moves by the velocity which is interpolated from the fluid velocity. In numerical results, we first verify several facts of the immersed boundary method and then consider a bubble immersed in an two-dimensional incompressible fluid. We observe the deformation of a bubble with different Capillary number in a shear flow. Moreover, we take the advantage of an equi-distributed technique to control the distribution of the Lagrangian markers uniformly. As expected, the numerical experiments with marker control technique have better performance in the area preservation than the case without it.