臺灣博碩士論文加值系統

本文以無網格方法所建立之二維數值模式，求解拉普拉斯方程式(Laplace equation)，模擬非線性波浪之自由液面變形及移動邊界造波。本數值模式主要架構為Wu and Chang (2011)發展之三維RBF(radial basis function)無網格模式，其特色是在邊界上同時滿足控制方程式，改善了以往RBF無網格法在邊界上的函數偏微分值不正確的問題。後經本研究將此模式修改為二維模式，並增加其造波及模擬移動邊界之功能後，進行一系列模擬討論其物理現象及模式適用性。
本研究之模式驗證共進行兩組模擬，分別為Beji and Battjes (1994)規則波通過潛堤之試驗及Lynett and Liu (2002)完全潛沒海底崩移造波。前者的模擬結果與試驗數據吻合良好。此外，本研究利用無網格模式之特性，進一步討論水質點運動軌跡特性；後者之模擬結果與Lynett and Liu (2002)之邊界積分法模式、一層及二層布氏模式結果比較，同樣達到良好的吻合度。
確認模式的適用性之後，本研究將此模式應用於模擬半潛沒海底崩移。半潛沒海底崩移即一崩移物體初始時由水面上滑落，與完全潛沒崩移造成之波浪特性並不相同。本研究主題共進行兩組模擬，分別討論不同的底床坡度及不同的崩移水平距離下，半潛沒海底崩移造波的傳遞情形與岸線變化的差異。最後，本文提出對於模擬結果的歸納討論，並對此數值模式之未來發展提出建議。

A two-dimensional numerical model using radial basis functions (RBFs) and collocation points for resolving the Laplace equation is presented in this study. This method is a general meshless method called RBF collocation method. The basic concept of RBF collocation method is to approximate the solution of a PDE as a linear combination of RBFs. The main framework of the present model is developed by Wu and Chang (2011), and is added with the wave-sending boundary, radiation boundary and ability for simulating the moving boundary problem by this study.
Two simulations are carried out for the model validation. First, regular waves propagating over a submerged breakwater are simulated. The results are compared with the experimental data, and the water particle trajectory is also discussed. The second one is waves generated by submerged landslide and the results are compared with other numerical solutions, such as BIEM and Boussinesq-type model. Fairly good agreements are observed in both of simulations.
Finally, the present model is applied to calculate the subaerial landslide-induced waves. Subaerial landslide on three plane slopes of different angles, which are 6, 15 and 30 degrees, with the same constant water depth at the end of the slopes is studied. Specifically, the landslide-induced wave propagation and shoreline motions are examined. Furthermore, the effects of various sliding horizontal distances along the same slope on induced-wave are also discussed.

中文摘要 I
Abstract II
致謝 III
目錄 IV
表目錄 VII
圖目錄 VIII
符號表 X
第一章 緒論 1
1.1 研究動機及目的 1
1.2 文獻回顧 3
1.2.1 無網格方法 3
1.2.2 海底崩移 6
第二章 理論基礎 7
2.1 控制方程式 7
2.2 自由液面邊界條件 8
2.3 底床邊界條件 9
2.4 側向邊界條件 9
2.5 初始條件 11
第三章 數值模式 12
3.1 模式簡介 12
3.2 幅狀基底函數 12
3.3 時間域之離散 13
3.4 配置點之條件 14
3.5 誤差控制 16
3.6 移動邊界 17
3.7 經驗參數 18
3.8 模式計算流程 20
第四章 模式驗證 21
4.1 固定邊界：規則波通過潛堤 21
4.1.1 模型配置 21
4.1.2 驗證結果 22
4.2 移動邊界：完全潛沒海底崩移 30
4.2.1 模型配置 30
4.2.2 驗證結果 34
第五章 半潛沒海底崩移 37
5.1 崩移物體幾何形狀 37
5.2 崩移物體運動速度 39
5.3 崩移物體參數設定 40
5.3.1 Case A：不同底床坡度之半潛沒海底崩移 40
5.3.2 Case B：不同崩移水平距離之半潛沒海底崩移 42
5.4 移動邊界模式設定 43
5.5 結果討論 44
5.5.1 Case A結果討論 44
5.5.2 Case B結果討論 54
第六章 結論與建議 60
6.1 結論 60
6.2 建議 62
參考文獻 63
附錄A 自述 67

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