| This thesis presents an implementation of a second-order accurate immersed interface method for computing incompressible immiscible two-fluids with different densities and viscosities. In the immersed interface method, a two-fluid problem is formulated as one set of governing equations and simulated on a fixed Cartesian grid. The effect of the two-fluid interface enters the formulation as a singular force and a numerical scheme at jump conditions. In this thesis, we will present the principal jump conditions, discuss the difficulties in implementing them, and provide a few options to overcome the difficulties. Finally, numerical results and comparisons are given to demonstrate the accuracy and efficiency of this method. |
