臺灣博碩士論文加值系統

本研究旨在探討Boussinesq equations，並發展一套數值模式，期能預測分析波浪傳遞之現象。文中以[2,2] Padé approximation推導以任意水深位置形式表示之Boussinesq equations，並比較以不同水深位置速度為變數時，其分散關係式、群波速及淺化梯度，並由其結果可知，控制相位速度誤差在5﹪的條件下時，其相對水深限制 可延伸到0.5。數值計算方法利用Fourth-order Adams-Bashforth-Moulton predictor-corrector scheme以及消波邊界條件求解Boussinesq equations，以增加數值計算之穩定性。最後並將數值計算結果與實驗數據及理論解，作一比較分析，以為本數值模式之驗證。

The purpose of this research is to develop a numerical model based on Boussinesq equations that can predict the wave transformation. By [2,2] Padé approximation, different velocity parameter Boussinesq equations are derived. The effects of different Boussinesq type equations on linear dispersion relations, group velocity and shoaling gradients were discussed. The limitation of on the applications of Boussinesq equations can be extended to 0.5 under suitable choice of the velocity parameter with the requirement of the difference of the phase velocities from calculation and from linear dispersion relation less than 5﹪. The fourth-order Adams-Bashforth-Moulton predictor-corrector scheme with proper absorbing boundary conditions was imposed as the basic numerical scheme. Finally, numerical results were verified with past experimental and theoretical results.

中文摘要Ⅰ
英文摘要Ⅱ
目錄Ⅲ
圖目錄Ⅴ
表目錄Ⅶ
符號說明Ⅷ
第一章緒論1
1-1 概述1
1-2 相關文獻回顧5
1-3 研究內容8
第二章理論分析10
2-1 控制方程式及邊界條件10
2-1-1 無因次化方程式及其邊界條件12
2-1-2 波浪勢流函數之垂直分佈函數13
2-1-3 微擾法15
2-2 分散關係式及淺化特性20
2-2-1 分散關係式21
2-2-2 群波速24
2-2-3 淺化梯度27
第三章數值方法29
3-1 基本方程式有限差分化30
3-1-1 基本方程式30
3-1-2 時間之離散式32
3-1-3 空間之離散式35
3-2 邊界條件37
3-2-1 入射波邊界條件38
3-2-2 完全反射邊界條件38
3-2-3 消波邊界條件39
3-3 穩定條件40
第四章模式驗證42
4-1 一維波浪傳遞數值模擬42
4-1-1 消波邊界條件測試42
4-1-2 孤立波43
4-1-3 波浪傳遞現象與相對水深限制47
4-1-4 潛堤測試51
4-2 二維波浪傳遞數值模擬54
第五章結論與建議56
參考文獻58
圖 目 錄
圖2-1空間座標示意圖10
圖2-2不同速度變數 與線性波理論之分散關係式曲線比較圖23
圖2-3不同速度變數 與線性波理論之相位速度誤差比較圖23
圖2-4不同速度變數 與線性波理論之群波速比較圖25
圖2-5不同速度變數 與線性波理論之群波速誤差比較圖26
圖2-6不同速度變數 淺化係數梯度與線性波之比較圖28
圖3-1座標格點位置圖37
圖3-2一為正向消波邊界條件示意圖41
圖4-1消波邊界處水面波形變化圖43
圖4-2孤立波（ ）數值解與理論解在不同計算時間時的空間位置比較圖45
圖4-3不同波高之孤立波波形比較圖46
圖4-4Conventional Boussinesq equations計算時間 時的波形剖面圖48
圖4-5Extended Boussinesq equations計算時間 時的波形剖面圖48
圖4-7Conventional Boussinesq equations在 的位置歷時波形變化比較圖50
圖4-8Extended Boussinesq equations在 的位置歷時波形變化比較圖50
圖4-9實驗潛堤配置圖51
圖4-10Case（2）波浪通過潛堤P3及P5位置之歷時波形變化圖53
圖4-11Case（4）波浪通過潛堤P3及P5位置之歷時波形變化圖53
圖4-12Case（6）波浪通過潛堤P3及P5位置之歷時波形變化圖53
圖4-13Ring test歷時波形變化圖55
表 目 錄
表1-1 波場模式之適用範圍表4
表4-1 潛堤實驗入射波浪條件表52

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