This thesis presents two methods for simulating flows over or inside complex elastic boundary. Scheme A is based on the feedback forcing concept, and scheme B is based on the immersed interface method. The immersed boundary generally dose not coincide with the grid point and these forcing procedures involve an interpolation scheme, since the boundary condition can be implemented on Eulerian grid directly. Scheme A is a more convenient method to simulate the elastic boundary problem. Its advantage is that the forcing value can be directly obtained form Lagrangian makers, but there is a smearing phenomenon on pressure field near interface. The smearing phenomenon will cause incorrect velocity at interface. Scheme B can determine the
sharp flow field, especially for pressure field. For leakage problem, scheme B always has better performance, because the velocity near interface can be evaluated more
correctly. A smooth curve is an important effect on stability. If the Lagrangian makers distribution isn't uniform, the force distribution can't be evaluated well. Here, we use periodic cubic spline to reconstruct Lagrangian makers with constant arc length and Fourier fitering to smooth the curve throughout each time step after moving boundary location. Numerical experiments also show that the stability limit can be improved if the distribution of Lagrangian makers is uniform. Four different test problems are simulated using present schemes, and scheme B has better performance.

This thesis presents two methods for simulating flows over or inside complex elastic boundary. Scheme A is based on the feedback forcing concept, and scheme B is based on the immersed interface method. The immersed boundary generally dose not coincide with the grid point and these forcing procedures involve an interpolation scheme, since the boundary condition can be implemented on Eulerian grid directly. Scheme A is a more convenient method to simulate the elastic boundary problem. Its advantage is that the forcing value can be directly obtained form Lagrangian makers, but there is a smearing phenomenon on pressure field near interface. The smearing phenomenon will cause incorrect velocity at interface. Scheme B can determine the
sharp flow field, especially for pressure field. For leakage problem, scheme B always has better performance, because the velocity near interface can be evaluated more
correctly. A smooth curve is an important effect on stability. If the Lagrangian makers distribution isn't uniform, the force distribution can't be evaluated well. Here, we use periodic cubic spline to reconstruct Lagrangian makers with constant arc length and Fourier fitering to smooth the curve throughout each time step after moving boundary location. Numerical experiments also show that the stability limit can be improved if the distribution of Lagrangian makers is uniform. Four different test problems are simulated using present schemes, and scheme B has better performance.

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