中文摘要

本文主要發展數值模擬不同造波機制之模式，藉以探討波浪生成與傳遞過程波形之演變及達穩定週期時的液面波傳變化及內部流場的運動特性。文中提出一個結合兩特定位置向量的組合曲線格網系統，用以瞬時貼合流場變動邊界。由此座標系統之微分幾何關係可計算貼壁座標系統幾何參數。文中以流函數為流場變數，並將Laplace方程式轉換至此曲線系統作為內部流場的控制方程式，搭配具有較大安定性、物理意義與更精確的有限解析法(Finite Analytic Method)來離散此控制方程式。同時，亦由有限差分法(Finite Difference Method)離散完全的自由液面邊界條件，與大幅度變位造波板條件。這些條件將由上述之瞬時貼壁座標系統直接在轉換之計算域上進行計算，再將所得結果對應回物理域上。本文經由數值疊代計算去獲得每個時階這些非線性聯立方程式的時階精確解。

數值造波的波形模擬結果，不但符合數值精度與效率且與近似理論解之結果及實驗量測有一致性。本模式經此驗證與比較長波與短波兩種波浪理論後，證明本模式適用於模擬一般自由液面問題。利用此組合動態座標系統與本文所用之數值處理方法可更方便於處理移動邊界之問題。而可延伸探討其他相關移動邊界之物理問題。

Abstract

In the thesis, I use a numerical model to simulate the wave generated by various types of wave maker and analyze the transient characteristics for the evolution of these waves to the quasi-steady waveform during propagation. A numerical hybrid grid system is obtained by combining two specific position vectors to construct the boundary-conforming, time-evolving, curvilinear coordinates over the fluid domain of interest. Using this coordinate system one can easily determine geometric coefficients from differential geometric relationship. The transformed Laplace equation in this grid system is then utilized to formulate the flow motion through the calculation of stream function in the numerical domain. The finite analytic discretization method applied to the present free-surface problem has the advantage of greater numerical stability, more physical sense and better accuracy over other discretization methods, e.g., the finite difference or finite element methods. Meanwhile, the complete free-surface boundary conditions and the large-displacement wave plate condition are specified and treated by using finite difference scheme on the moving boundary. Nonlinear coupling in the governing equation and these associated boundary conditions is therefore necessarily taken care by means of iterative procedure to seek the time-accurate solution at each time step.

The numerical result calculated by this wave model shows not only accurate and efficient solution but also measurements and other approximate analyses. I validated the simulated result in comparison with both short-wave and long-wave theories. It is concluded that the suggest numerical model developed in the present study has good capability to treat the general free-surface problems in all. The transient boundary-fitted grid system and associated numerical techniques enable one to treat those with boundary in deformable motion and will also give a reasonable extension to the application of other moving-boundary problems.

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