# 臺灣博碩士論文加值系統

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 以數值模擬方法研究流體經過雙橋墩流場變化。此方法使用最小平方有限元素法求解淺水波方程式。從模擬結果得知，接近橋墩時水深會壅起而過橋墩後方水深會下陷。當雙橋墩間距增加時，其干涉現象會由大逐漸變小。當兩橋墩間距超過4倍的直徑時，干涉現象可以忽視的。對於縱向排列的雙橋墩，干涉現象會較小，而其水深的分布也會類似單一橋墩現象。兩橋墩之間的水深隨著兩橋墩間距的增加水深會降低。本文研究，水深分布可有效地模擬和可能壅起的水體預測。希望結果能為水利工程學界被廣泛設計應用。
 A numerical simulation of the flow pass dual piers of a bridge has been presented in this study. The least-squares finite element method is employed for solving the governing shallow water equations. From the simulation results, it can be concluded that the water depth is accumulated proximal to the pier and drops immediately after the pier. The effect of the interference caused by the dual piers is strong and become weaker as the distance between the piers is increased. When the space between two piers is more than four times of the diameter of the pier, the effect of the interference is negligible. For the case of dual piers formed in a line along the flow direction, the effect of interference is small and the formation of the water depth is very similar to the distribution of a single pier. The water depth between two piers is lowered as the distance between piers increasing. In this study, the water depth distribution can be effectively simulated and the possible accumulation of water body is calculated. It is hoped that the results canbe used for the design purpose for the hydraulic engineering.
 本 文 目 錄第一章� 緒論........................................................................011-1前言.........................................................................011-2研究目的與方法...............................................................021-3文獻回顧......................................................................04第二章� 理論分析....................................................................102-1 LSFEM簡介.................................................................102-2理論推導...................................................................112-3淺水波方程式簡介...............................................................142-3-1最小平方有限元素法應用於淺水波方程式............................162-4 共軛梯度法介紹(Conjugate Gradient Method) .....................222-4-1元素-元素技巧（Element-by-Element Technique）...................232-4-2共軛梯度法(conjugate Gradient Method)簡介.......................242-5庫倫數(CFL)條件.........................................................................26第三章� 模式建立及邊界條件設定.........................................283-1單一橋墩流場驗證.............................................................28模式建立.........................................................................28邊界條件設定.........................................................................303-2具自由液面流體受結構物影響之數值驗證..............................30模式建立.........................................................................30初始條件設定.........................................................................31邊界條件設定.........................................................................31第四章� 結果與分析.........................................................................364-1單一橋墩模擬結果與分析.......................................................364-2雙橋墩模擬結果與分析.......................................................374-3縱向雙橋墩模擬結果與分析...........................................................394-4 單一橋墩與雙橋墩間模擬結果分析及比較..............................41第五章� 結論與建議.........................................................................435-1結論.........................................................................435-2建議.........................................................................44參考文獻.........................................................................46圖 目 錄圖1-1流體流經圓柱所產生的分離現象及尾流渦( Morkovin 1964).. 05圖1-2各種雷諾數值下之圓柱尾流型態（ Morkovin 1964）.............06圖3-1-1網格示意圖(Yulistiyanto 等, 1998) ........................................29圖3-1-2 網格示意圖...............................................................................29圖3-1-3邊界示意圖...............................................................................30圖3-2-1單一橋墩滑動邊界示意圖 .....................................................32圖3-2-2單一橋墩非滑動邊界示意圖圓柱上之速度設為零 .............32圖3-2-3並排雙橋墩間距示意圖 .........................................................33圖3-2-4縱向雙橋墩間距示意圖 .........................................................34圖3-2-5單一橋墩網格示意圖 .............................................................34圖3-2-6並排雙橋墩網格示意圖(以2D間距) ....................................35圖3-2-7縱向雙橋墩網格示意圖(以2D間距) .......................................35圖4-1-1速度向量圖(Yulistiyanto 等, 1998) .......................................50圖4-1-2速度向量圖................................................................................50圖4-1-3水深變化圖(Yulistiyanto 等, 1998) .........................................51圖4-1-4水深變化圖................................................................................51圖4-1-5 滑動邊界與非滑動邊界(單一橋墩)水深變化 T=4時間4秒水深變化滑動邊界(a)2D示意圖(c) 3D示意圖非滑動邊界(b)2D示意圖(d) 3D示意圖.................52圖4-1-6 滑動邊界與非滑動邊界(單一橋墩)水深變化 T=6時間6秒水深變化滑動邊界(a)2D示意圖(c) 3D示意圖非滑動邊界(b)2D示意圖(d) 3D示意圖 .................53圖4-1-7 滑動邊界與非滑動邊界(單一橋墩)流線變化 T=12 .............54圖4-1-8 明顯的看出滑動邊界圓柱下游後方不會有渦度產生 .........54圖4-1-9非滑動邊界單一橋墩T=42~56秒間的橋墩後方波街變化 .56圖4-1-10 單一橋墩選一間段時間及P點位置(6,0)與垂直速度的關係 圖 Time step 850~1150(t=42.5~57.5) ...................................57圖4-1-11 雙橋墩間距1.25倍選一間段時間及P點位置(6,0)與垂直速度的關係圖Time step 850~1150(t=42.5~57.5) ......................57圖4-1-12 雙橋墩間距1.5倍選一間段時間及P點位置(6,0)與垂直速度的關係圖Time step 850~1150(t=42.5~57.5) .........................58圖4-2-1 滑動邊界與非滑動邊界(雙圓柱橋墩1.25倍)水深變化 T=4時間4秒水深變化滑動邊界(a)2D示意圖(c) 3D示意圖非滑動邊界(b)2D示意圖(d) 3D示意圖 ...............59圖4-2-2 滑動邊界與非滑動邊界(雙圓柱橋墩1.25倍)水深變化 T=6時間6秒水深變化滑動邊界(a)2D示意圖(c) 3D示意圖非滑動邊界(b)2D示意圖(d) 3D示意圖 ...............60圖4-2-3 滑動邊界與非滑動邊界(雙橋墩間距1.5倍)水深變化 T=4時間4秒水深變化滑動邊界(a)2D示意圖(c) 3D示意圖非滑動邊界(b)2D示意圖(d) 3D示意圖 ...............61圖4-2-4滑動邊界與非滑動邊界(雙橋墩間距1.5倍)水深變化 T=6時間6秒水深變化滑動邊界(a)2D示意圖(c) 3D示意圖非滑動邊界(b)2D示意圖(d) 3D示意圖 ...............62圖4-2-5 滑動邊界與非滑動邊界(雙橋墩間距2倍)水深變化 T=4時間4秒水深變化滑動邊界(a)2D示意圖(c) 3D示意圖非滑動邊界(b)2D示意圖(d) 3D示意圖 ...............63圖4-2-6滑動邊界與非滑動邊(雙橋墩間距2倍)水深變化 T=6時間6秒水深變化滑動邊界(a)2D示意圖(c) 3D示意圖非滑動邊界(b)2D示意圖(d) 3D示意圖 ...............64圖4-2-7 滑動邊界與非滑動邊界(雙橋墩間距3倍)水深變化 T=4時間4秒水深變化滑動邊界(a)2D示意圖(c) 3D示意圖非滑動邊界(b)2D示意圖(d) 3D示意圖 ...............65圖4-2-8 滑動邊界與非滑動邊界(雙橋墩間距3倍)水深變化 T=6時間6秒水深變化滑動邊界(a)2D示意圖(c) 3D示意圖非滑動邊界(b)2D示意圖(d) 3D示意圖 ...............66圖4-2-9 滑動邊界與非滑動邊界(雙橋墩間距4倍)水深變化 T=4時間6秒水深變化滑動邊界(a)2D示意圖(c) 3D示意圖非滑動邊界(b)2D示意圖(d) 3D示意圖 .................67圖4-2-10 滑動邊界與非滑動邊界(雙橋墩間距4倍)水深變化 T=6時間6秒水深變化滑動邊界(a)2D示意圖(c) 3D示意圖非滑動邊界(b)2D示意圖(d) 3D示意圖 ...................68圖4-2-11 非滑動邊界(雙橋墩間距1.25倍)流線變化 ........................70圖4-2-12 非滑動邊界(雙橋墩間距1.5倍)流線變化 ..........................71圖4-2-13 非滑動邊界(雙橋墩間距2倍)流線變化 .............................72圖4-2-14非滑動邊界(雙橋墩間距3倍)流線變化 ..............................73圖4-2-15非滑動邊界(雙橋墩間距4倍)流線變化 ..............................75圖4-3-1 縱列雙橋墩1.25倍水深變化4秒(a)2D示意圖(b)3D示意圖及A、B、C點水深高 ...................................................75圖4-3-2 縱列雙橋墩1.25倍水深變化5秒(a)2D示意圖(b)3D示意圖及A、B、C、D、E點水深高 ......................................75圖4-3-3 縱列雙橋墩1.25倍水深變化6秒(a)2D示意圖(b)3D示意圖及A、B、C、D、E、F點水深高 ...............................76圖4-3-4 縱列雙橋墩1. 5倍水深變化4秒(a)2D示意圖(b)3D示意圖及A、B、C點水深高 ...................................................76圖4-3-5 縱列雙橋墩1. 5倍水深變化5秒(a)2D示意圖(b)3D示意圖及A、B、C、D、E點水深高 ....................................77圖4-3-6 縱列雙橋墩1. 5倍水深變化6秒(a)2D示意圖(b)3D示意圖及A、B、C、D、E、F點水深高 .................................77圖4-3-7 縱列雙橋墩2倍水深變化4秒(a)2D示意圖(b)3D示意圖及A、B、C點水深高 .....................................................78圖4-3-8 縱列雙圓柱2倍水深變化5秒(a)2D示意圖(b)3D示意圖及A、B、C、D、E、G點水深高 ................................78圖4-3-9 縱列雙橋墩2倍水深變化6秒(a)2D示意圖(b)3D示意圖及A、B、C、D、E、F、G點水深高 .........................79圖4-3-10 縱列雙橋墩2倍水深變化7秒(a)2D示意圖(b)3D示意圖及A、B、C、D、E、F點水深高 .................................79圖4-3-11 縱列雙橋墩3倍水位變化4秒(a)2D示意圖(b)3D示意圖及A、B、C點水深高 ...................................................80圖4-3-12 縱列雙橋墩3倍水位變化5秒(a)2D示意圖 (b)3D示意圖及A、B、C、D點水深高 .............................................80圖4-3-13 縱列雙橋墩3倍水位變化6秒(a)2D示意圖(b)3D示意圖及A、B、C、D、E、G點水深高 ..............................81圖4-3-14 縱列雙橋墩3倍水位變化7秒(a)2D示意圖(b)3D示意圖及A、B、C、D、E、F、G點水深高 ........................81圖4-3-15 縱列雙橋墩4倍水位變化4秒(a)2D示意圖(b)3D示意圖及A、B、C點水深高....................................................82圖4-3-16 縱列雙橋墩4倍水位變化5秒(a)2D示意圖(b)3D示意圖及A、B、C、D點水深高 ............................................82圖4-3-17 縱列雙橋墩4倍水位變化6秒(a)2D示意圖(b)3D示意圖及A、B、C、D點水深高 ..............................................83圖4-3-18 縱列雙橋墩4倍水位變化7秒(a)2D示意圖(b)3D示意圖及A、B、C、D、E、G點水深高 ...............................83圖4-3-19 縱列雙橋墩4倍水位變化8秒(a)2D示意圖(b)3D示意圖及A、B、C、D、E、F、G點水深高 ............................84圖4-3-20 縱列雙橋墩1.25倍流線變化15秒 .....................................84圖4-3-21 縱列雙橋墩1.25倍流線變化25，35，45，60，70，80秒 ..86圖4-3-22縱列雙橋墩1.5倍流線變化15，25，35，45，60，70，80秒 ..........................................................................................................87圖4-3-23 縱列雙橋墩2倍流線變化15，25，35，50，70，80秒 ...89圖4-3-24 縱列雙橋墩3倍流線變化15，25，40，55，70，80秒 ...90圖4-3-25 縱列雙橋墩4倍流線變化15，25，40，55，70，80秒 ...92圖4-4-1橫向雙橋墩各不同間距間時間與水深之比較 ......................92圖4-4-2單一橋墩在T=40秒之水深變化圖.........................................93圖4-4-3單一橋墩在T=50秒之水深變化圖........................................93圖4-4-4單一橋墩在T=40秒之水深變化3D示意圖.........................94圖4-4-5單一橋墩在T=50秒之水深變化3D示意圖.........................94圖4-4-6橫向橋墩間距2倍T=30秒以中心線為主(y=0)之水深變化圖..................................................................................................................94圖4-4-7橫向橋墩間距2倍T=30秒以橋墩後方(y= )之水深變化圖..................................................................................................................95圖4-4-8橫向橋墩間距4倍T=30秒以中心線(y=0)之水深變化圖......95圖4-4-9橫向橋墩間距4倍T=30秒以橋墩後方(y= )之水深變化圖..................................................................................................................96圖4-4-10縱向橋墩間距1.25倍T=30秒以中心線為主(y=0)之水深變化圖..........................................................................................................96圖4-4-11縱向橋墩間距2倍T=30秒以中心線為主(y=0)之水深變化圖..................................................................................................................97圖4-4-12縱向橋墩間距4倍T=30秒以中心線為主(y=0)之水深變化圖..................................................................................................................97表 目 錄表4-1 流場在時間T=4所發生的水深變化表....................................98表4-2 流場在時間T=6所發生的水深變化表....................................99表4-3 流場在時間T=4所發生的水深變化表....................................99表4-4 流場在時間T=5所發生的水深變化表...................................100表4-5 流場在時間T=6所發生的水深變化表...................................100
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 1 定量流流況下同心圓柱型上下游連續橋墩局部沖刷之研究 2 變量流流況下非均勻縱列雙橋墩局部沖刷之研究 3 二維淺水波在不規則底床運行之研究 4 利用淺水波方程式與布氏方程式模擬波浪通過潛堤之比較 5 利用淺水方程式研究地形對波浪變形之影響 6 最小平方有限元素法在二維淺水波方程式之數值模擬 7 淺水波方程式應用於彎曲河道之數值模擬 8 山谷中潰壩衝擊水工結構物之現象探討

 1 郭鴻基、吳俊傑、李清勝，中華民國九十年十二月：天搖地動—颱風研究的挑戰。科學發展月刊第二十九卷第十二期。 2 [2]關維雅，1991，“中日合院型住宅空間結構之比較研究”，「建築學報」第四期，中華民國建築學會，頁19-42。

 1 圓柱橋墩結構之計算流體力學模擬研究 2 局部化無網格徑向基底函數數值法於淺水方程式之應用 3 結合美國文化主題在大學英文課之影響 4 調查使用英漢字典對英文寫作能力評量之影響 5 微動平台結構之動態特性分析 6 液靜壓封閉式軸承使用雙向補償之特性分析 7 模內轉印射出成型薄膜滯熱對產品翹曲影響之研究 8 高溫薄型玻璃模造技術建置與製程條件控制之研究 9 顯示器塑膠底座幾何結構補強肋之研究 10 田口方法於射出成型機之頂出力與熱澆道澆口冷卻系統之研究 11 油浸式變壓器散熱之研究 12 滑蓋手機之制動彈簧設計 13 彈體以高速撞擊鋼纖維混凝土之物理行為分析 14 利用田口法設計LCD膠框強度的模擬分析 15 LCD液晶面板熱變形模擬研究

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