臺灣博碩士論文加值系統

本研究以RANS (Reynolds Averaged Navier-Stokes equations) 方程式建立二維數值模式，結合k −ε 紊流閉合模式，模擬波浪通過斜坡後碎波流場的變化情形，自由液面的追蹤則採用流體體積法 (Volume of Fluid，VOF) 耦合分段線性界面重建法 (Piecewise Linear Interface Construction，PLIC) 液面捕捉方式處理複雜之碎波液面變形。本研究選取Ting 與Kirby (1994) 的溢波型試次實驗資料來校驗模式的適用性與正確性。結果顯示於波浪水位變化與速度分佈的模擬皆呈現良好的一致性，顯示本模式能夠有效地模擬波浪碎波前後，從淺化過程到碎波及能量消散階段的水理變化特性。

The purpose of the present study is to develop a two-dimensional numerical
model based on RANS (Reynolds Averaged Navier-Stokes) equations combined
with a second-order k − ε turbulence closure model. The wave breaking process
such as water waves travel over a sloping bottom is investigated. To track free
surface movements, the VOF (Volume of Fluid) coupled with PLIC (Piecewise Linear Interface Construction) method is employed. To ensure the accuracy of the numerical model, numerical results were compared with Ting and Kirby’s (1994) experiment data for the case of spilling breaker. Good agreement between numerical results and experimental data has been observed for shoaling and breaking cnoidal
waves on a sloping bottom in terms of free surface profiles and mean velocities.

中文摘要　I
Abstract　II
誌謝　III
目錄　V
表目錄　VII
圖目錄　VIII
符號說明　X
第一章　緒論　1
1.1　研究動機與目的　1
1.2　前人研究　5
1.2.1　碎波流場與紊流之試驗研究　5
1.2.2　碎波流場與紊流之數值模擬研究　6
1.2.3　自由液面捕捉方式　7
1.3　研究架構　10
第二章　理論基礎　12
2.1　控制方程式　12
2.2　k −ε 紊流模式　14
2.3　初始條件　19
2.4　邊界條件　19
2.4.1　上游邊界條件　20
2.4.2　下游邊界條件　21
2.4.3　底床結構物邊界條件　22
2.4.4　自由液面邊界條件　23
第三章　數值模式　25
3.1　格網變數之配置　25
3.1.1　交錯格網　25
3.1.2　格網類別　26
3.2　離散方程式　27
3.2.1　對流項與擴散項之離散　30
3.2.2　壓力項之離散　31
3.2.3　時間項之離散　31
3.3　壓力疊代法則　32
3.3.1　滿格網壓力修正量　33
3.3.2　自由液面格網壓力修正量　34
3.4　自由液面　36
3.5　計算流程　39
第四章　結果與討論　41
4.1　試驗配置與條件　41
4.2　水位變化驗證　42
4.3　流速驗證　45
4.4　碎波過程之紊流傳輸機制　48
第五章　結論與建議　60
5.1　結論　60
5.2　建議　62
參考文獻　63

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