為了模擬複雜的柔性柱體擺盪，本研究利用假頻譜矩陣元素法結合直接施力沉浸邊界法開發出一套流固耦合的計算流體力學數值模型，並且使用了區域分解法和座標轉移將其優化。首先，透過自由流通過固定圓柱的模擬，確認此數值模式的準確性與收斂性。而使用區域分解法分割出小區域的流場也使判斷固體區間上具有更好的效果。接著，我們模擬自由流經過剛性圓柱所引起的振動現象。在不同雷諾數與約化速度下，觀察鎖相放大現象的區間以及最大振幅和頻率，並與其他研究相比。而當固體在網格之間振盪時，坐標變換則可以改善直接施力沈浸邊界法處理固體在不同網格情況下積分合力時所產生的雜訊。最後我們模擬低雷諾數下流體通過無限長的柔性圓柱，考慮計算的可行性，此研究假設圓柱為短波長的振盪，以及使用週期性邊界條件進行計算，研究圓柱振盪與流動模式的問題。再給定初始位移下，電纜震盪在前期產生穩定的駐波響應，並逐漸轉為行進波響應，此物理現象與其它研究結果一致。而駐波響應產生跨度交織的渦流模式，行進波響應則產生了斜向脫落的渦流。此研究測試不同相速度後，由於相速度影響了電纜的自然頻率與波長，最終統整出不同相速度下的渦流模式及振盪模式的轉變。

The present study simulates the complex oscillation of a long flexible cylinder. An in-house numerical model was developed using pseudopsectral methods coupled with the direct-forcing immersed boundary (DFIB) method to investigate this phenomenon. The domain decomposition method and coordinate transformation were also applied to optimize the proposed numerical model. The model was validated first by simulations of flow through a fixed cylinder in a free stream. The preciseness and convergence analysis are presented in the validation section. The domain decomposition method was used to divide the computational domain into smaller domains. A solid body can be identified more precisely using the adopted PSME-DFIB model. This model was used to simulate the flow-induced vibration of an elastically mounted rigid cylinder. The variation of vibration frequency and maximum amplitude with respect to Reynolds number and reduced velocity was investigated in the lock-in region and compared against published results. When solids move through grids, the coordinate transformation can eliminate noise in the resultant force, as determined by the numerical integral. In addition, the in-house model was used to investigate the flow-induced vibration of an infinitely long flexible cylinder at various wavelengths, cylinder tensions and lower Reynolds numbers. A short-wavelength cylinder was considered due to the feasibility of simulations. Periodic boundary conditions were utilized. The effects of cylinder vibration on the flow patterns were also explored in detail. Given the initial displacement, the cylinder vibration was produced a stable standing wave response in the early stage, and gradually turned into a traveling wave response. this physical phenomenon is consistent with others experimental and numerical solution. An intertwined vortex is produced the standing wave response produces. The vortex of the traveling wave occurs a oblique shedding. Finally, this study investigated different phase velocities. Since the phase velocities affected the natural frequency and wavelength of the cylinder, vortex patterns and their transformation at different phase velocity were summarized.

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