本研究主要採用無限長分歧路徑複變數邊界元素法模擬二維容器受到水平外力時產生的沖激現象。所謂沖激問題意指當容器受到外力振動，內部液體的振盪行為。文中假設液體須滿足勢流理論，且有足夠的邊界條件，可以求解自由液面之勢位；自由液面的位置和液面上的邊界條件則隨著時間不斷更新。應用無限長分歧路徑複變數邊界元素法可求出邊界上勢位法向導微及切向導微，藉此求得更新後相關的物理量。數值試驗結果顯示，使用奇異性較低的核函數，所得到的結果較使用奇異性較高的核函數的結果要更為理想。本文將以兩種形狀的水槽為例，分別計算其受到水平外力時，水槽內部液體自由液面的運動情況。

摘要 I
目錄 III
圖目錄 V
第一章 導論 1
1.1 研究動機及背景 1
1.2 研究內容及方法 4
1.3 本文架構 5
第二章 沖激問題基本理論分析 7
2.1 基本概論 7
2.2 控制方程式 8
2.3 邊界條件 9
2.4 時間函數處理 11
第三章 複變數邊界元素法的理論架構 14
3.1物理問題 14
3.2 基本理論 14
3.3 邊界物理量離散化 17
3.3.1 曳引力採用常元素 19
3.3.2 位移採用常元素 20
3.4 分歧路徑 (Branch cut) 20
3.4.1 簡介 20
3.4.2 無限長分歧路徑 21
3.5複變數邊界元素法之應用 23
第四章 數值模擬方法及算例 33
4.1 複變數積分式之應用 33
4.2 時間函數之處理 34
4.3 Euler法時間增量 36
4.3.1 邊界物理量 36
4.3.2 Euler法計算步驟 37
4.3.3 勢位微分的座標轉換 38
4.4 數值技巧 39
4.4.1 元素節點速度之決定 39
4.4.2 邊界形狀角點之決定 40
4.5 數值算例 41
4.5.1 矩形水槽 41
4.5.2 梯形水槽 42
第五章 結論及建議 56
參考文獻 58

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