Abstract
This thesis uses immersed interface method to simulate flows with elastic boundary and the unclosed elastic boundary problem. Unusually, here we develop the new model with finite volume method in staggered grids. It also can achieve equivalent accuracy to finite difference method with less jump conditions. In order to improve the accuracy of pressure, we have to derive a pressure correction equation for the fractional step method. To maintain the uniformity of the intersection locations for a moving boundary problem, we use cubic spline interpolation to reconstruct Lagrangian markers with constant arc length and Fourier filtering to smooth the curve throughout each time step after moving location. Numerical experiments also show the stability limit can be improved if the distributions of Lagrangian markers are uniform. Several problems are simulated by using the present method.