臺灣博碩士論文加值系統

本文主旨為發展二維黏性數值波浪模式，模擬孤立波通過實際海底底床後，於海堤上溯升及越波之演變。為模擬真實流體的運動情形，本模式擬求解時變的RANS方程與紊流模式，結合質點等位函數法追蹤複雜的自由液面變化，並於卡氏坐標系統下，採用沉浸邊界法 (Immersed Boundary method) 處理不規則固體邊界附近的流場演變機制。本模式經由拉穴流運動 (cavity flow problem)、旋轉缺口圓盤問題 (Zalesak’s problem) 及均勻流通過圓柱等數值試驗，測試本模式的準確性，皆獲得不錯之結果。最後，本文應用此模式模擬不同入射條件之孤立波衝擊台東近岸海堤後 (台東、富岡及三和) 波浪淺化、溯升（降）及越波情形。探討波浪入射波高、入射距離及海堤高度等對於波浪在海堤上溯升或越波的影響。

In present study a 2-D numerical viscous wave model was developed and applied to represent propagation of a solitary wave over a seawall on a real sea bed including run-up or overtopping phenomena. The numerical model solved the unsteady, two dimensional Reynolds Average Navier-Stokes (RANS) equation and the turbulent model ( model) for simulating the realistic fluid. A hybrid particle level set method was incorporated to capture the complex free surface. An immersed boundary method was adapted to present the behavior of fluid flow in the vicinity of irregular solid boundary in the Cartesian coordinate system. The numerical results were demonstrated by a serious of numerical experiments, such as the Zalesak’s problem, cavity flow problem, and a uniform flow pass through a cylinder. Finally, the present wave model was conducted to simulate the surface evolution as a solitary wave attacked the seawall of Taidung, Fugang and Sanhe of Taidung Taiwan. Including wave shoaling, run-up, run-down and overtopping phenomena were observed in numerical results and the relationships between run-up height and incident wave heights, the distance from wave incident to a seawall etc. were discussed briefly.

第一章 緒論
1-1 研究動機 1
1-2 相關文獻 2
1-2-1 溯升之前人研究 2
1-2-2 越波之前人研究 3
1-2-3 數值模式之相關研究 3
1-3 本文架構 6
第二章 理論分析
2-1 控制方程式 7
2-2 無因次化處理 10
2-3 等位函數法 (Level Set Method) 12
2-4 質點等位函數法 (Particle Level Set Method) 13
2-5 沉浸邊界法 (Immersed Boundary Method) 14
2-6 初始條件和邊界條件 15
第三章 數值方法
3-1 計算網格配置 19
3-2 控制方程式之離散化 20
3-3 速度與壓力之耦合 23
3-4 自由液面邊界條件的處理 25
3-5 計算流程 31
3-5-1 模式計算流程 31
3-5-2 數值模式流程圖 32
第四章 結果與討論
4-1 數值模式驗證 33
4-1-1 等位函數法之驗證 33
4-1-2 本文模式模擬流場之驗證 34
4-1-3 沉浸邊界法之驗證 34
4-2 實際應用之案例 36
4-2-1 波浪經過平坦底床後之溯升 36
4-2-2 波浪通過斜坡後之越波 36
4-2-3 長浪於台東縣沿岸海堤的溯升與越波 36
第五章 結論與建議
5-1 結論 51
5-2 建議 52
參考文獻 53

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