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研究生:胡瑋靖
研究生(外文):Wei-ChingHu
論文名稱:利用無網格法模擬未碎波之孤立波於斜坡上的演化及溯升
論文名稱(外文):Simulation of nonbreaking solitary wave evolution and runup on plane beaches using meshless method
指導教授:蕭士俊蕭士俊引用關係
指導教授(外文):Shih-Chun Hsiao
學位類別:碩士
校院名稱:國立成功大學
系所名稱:水利及海洋工程學系碩博士班
學門:工程學門
學類:河海工程學類
論文種類:學術論文
論文出版年:2012
畢業學年度:100
語文別:中文
論文頁數:88
中文關鍵詞:無網格法徑向基底函數孤立波溯升
外文關鍵詞:Meshless MethodRadial basis functionSolitary waveRun-up
相關次數:
  • 被引用被引用:1
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  • 下載下載:33
  • 收藏至我的研究室書目清單書目收藏:0
本文利用一種新的數值方法,無網格法(Meshless method)去模擬一個二維無黏性數值水槽模式,利用徑向基底函數(Radial Basis Function, RBF) 的線性組合擬合流體速度勢,進一步去模擬利用活塞式造波板(Piston-type Wavemaker)造出一系列不同條件下的孤立波。
為了確認此新的數值模式的適用範圍以及準確性,本文使用三個不同條件的數值模擬進行驗證,並將模擬的數值結果與前人之實驗資料做比對。其中包括孤立波於一斜坡(斜率為s=1:2.75)上自由液面的變化與最大溯升高度;另外一個則是不同非線性量下的孤立波入射至另一個的斜坡(斜率為s=1:1.732)時,在不同時刻下的流場變化;最後則是當一個孤立波在水平底床上行進時,其質點隨著水深的不同,有著不同的移動軌跡。經由數值模擬的結果與實驗資料做比對,有不錯的吻合度。
在驗證數值模式的準確性之後,為了瞭解孤立波溯升時的流場特性,我們利用這個新的方法,模擬孤立波在未碎波的情況下,在水平渠道上行進並入射至斜坡上,進行一系列有關最大溯升高度、能量變化、質點軌跡以及流場變化等等物理現象的探討。而海嘯又有許多種的型態,Liu et al. (2005)證實在南亞海嘯時,觀察到海嘯波可能由一個甚至到三個的波,連續朝著海岸傳播,所以可以發現海嘯不只是只有單一個孤立波構成;所以我們進一步的去探討當兩個孤立波產生於同一個渠道時,做相同的物理現象探討。
In this paper, a new numerical method, named Meshless Method, is proposed to solve the two-dimensional potential flow theory using the linear combination of the radial basis function (RBF) to resolve the velocity potential in a Lagrangian coordinate system. Also, we construct a piston-type wavemaker into the present numerical model to generate desired waves, such as a solitary wave.
To validate the present numerical model, it is necessary to carry out numerical experiments to compare with available experimental data in literatures. The first validate is demonstrated for a solitary wave run-up on a 1:2.75 slope. The modeled time histories of the free surface elevation and calculated maximum run-up height are compared with measurements. The second one is to simulate a solitary wave passes over a 1:1.732 slope. The comparisons between measurements and numerical results are performed for the instantaneous free surface elevation and velocity profiles. Finally, solitary wave propagation in a constant wave depth is carried out to illustrate the trajectories of fluid particles and also compare with measurements. The numerical results fit the measurements fairly well.
Additional numerical experiments are performed in order to have a deep investigation on the wave dynamics during the process of solitary wave run-up on a steep beach. The main attentions would be paid on the effects of the maximum run-up height, energy variations, trajectories of fluid particles and velocity fields. To extend the present model to simulate the propagation of tsunami-like long waves, a train of successive two solitary waves over a slope is consider to discuss the effect of wave dynamics between an isolated and successive two solitary waves.
摘要 ..............................................................................................................................I
ABSTRACT ............................................................................................................... II
誌謝 ........................................................................................................................... IV
目錄 ............................................................................................................................ V
圖目錄 ..................................................................................................................... VII
表目錄 ....................................................................................................................... XI
符號表 ..................................................................................................................... XII
第一章 序論 ............................................................................................................... 1
1-1前人研究 ........................................................................................................... 2
1-1-1無網格法 (Meshless method) ................................................................... 2
1-1-2孤立波(Solitary wave) ............................................................................... 4
1-1-3溯升(Runup) ............................................................................................... 5
1-1-4兩連續孤立波(Two successive solitary waves) ........................................ 6
1-2本文組織 ........................................................................................................... 8
第二章 理論基礎....................................................................................................... 9
2-1控制方程式(Governing equation) .................................................................... 9
2-2初始條件與邊界條件 ..................................................................................... 10
2-2-1初始條件(Initial condition) ...................................................................... 10
2-2-2自由液面的邊界條件(Boundary condition at the free surface) .............. 10
2-2-3固體邊界的邊界條件(Boundary condition on a solid boundary) ........... 11
第三章 數值方法..................................................................................................... 12
3-1徑向基底函數 ................................................................................................. 12
3-2傳統RBF配置方法解PDE ........................................................................... 13
3-3本研究的RBF配置方法 ............................................................................... 14
3-4計算域所需的佈點限制 ................................................................................. 16
3-5求解的型式 ..................................................................................................... 17
3-6時間項之處理 ................................................................................................. 18
3-7模式計算流程 ................................................................................................. 19
第四章 模式驗證..................................................................................................... 21
4-1 造波能力 ........................................................................................................ 23
4-2 孤立波之溯升與傳播過程 ............................................................................ 26
4-2-1 孤立波的波高計及海岸線驗證 ............................................................. 27
4-2-2 孤立波的流場驗證 ................................................................................. 32
第五章 結果與討論................................................................................................. 39
5-1孤立波的最大溯升高 ..................................................................................... 39
5-2孤立波的溯升與溯降能量變化 ..................................................................... 53
5-3孤立波軌跡 ..................................................................................................... 60
第六章 結論與建議................................................................................................. 83
6-1 結論 ................................................................................................................ 83
6-2 建議 ................................................................................................................ 85
參考文獻 ................................................................................................................... 86
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