| 中文摘要 |
非線性波浪傳遞問題以及波浪與結構物互制問題一直是海洋工程、海岸工程與海洋能源領域非常重要的研究課題，本論文採用奇異邊界法（singular boundary method）開發二維數值波浪水槽，用以研究非線性波浪傳遞之特性，以及波浪與潛堤互制之問題。奇異邊界法是一種新開發的邊界類無網格法（meshless method），能省略網格產生與數值積分等耗時的工作，只需要邊界點位就可以進行電腦模擬，是非常簡單且高效率的電腦模擬方法，特別適合用以模擬自由水面等移動邊界問題。除了採用奇異邊界法進行方程式空間離散之外，本模式採用四階預測校正法進行方程式之時間離散，以獲得穩定與準確之電腦模擬結果。本研究使用半拉格朗日法計算點位的移動量、使用斜坡函數穩定造波機產生之入射波，也採用海綿層耗散波浪能量，以避免任何反射波浪重新進入水槽。本研究結合以上數種數值分析方法開發完成一高效率數值波浪水槽，並以四個案例驗證此無網格法模式之高度準確性，模擬結果與前人研究結果比對非常一致，並且採用不同總點數與時間間隔進行電腦模擬，以驗證本論文所開發無網格法模式之穩定性與一致性。
To study the propagation of nonlinear water waves and the interactions between waves and submerged structures plays an important role in marine engineering and near-shore engineering. Thus, in this paper, a numerical wave flume, based on the singular boundary method (SBM), is proposed to study the free-surfaces problems of nonlinear water waves. The SBM is a newly-developed boundary-type meshless method and can truly avoid the time-consuming tasks of mesh generation and numerical quadrature. Since only boundary nodes are needed to implement the SBM, the SBM is very suitable for dealing with the moving-boundary problems of nonlinear water waves. In addition to the spatial discretization by the SBM, the fourth-order predictor-corrector method is adopted for the temporal discretization of numerical wave flume and the semi-Lagrangian approach is responsible for calculation of nodal movements. The ramping function is used for stably generating the incident wave, while the sponger layer is deployed in the outlet to avoid any reflection of water wave. Thus, a highly-efficient numerical wave flume is formed in this paper by combining the SBM, the predictor-corrector method, the semi-Lagrangian approach, the ramping function and the sponge layer. Four numerical examples are provided so as to verity the merits of proposed numerical wave flume. Different numbers of total nodes and different time increments are examined to demonstrate the consistency and the stability of the proposed numerical wave flume. |
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