雙向流固耦合移動邊界法發展及其於山崩海嘯之研究

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姓名

莊美惠(Mei-hui Chuang) 查詢紙本館藏

畢業系所

水文與海洋科學研究所

論文名稱

雙向流固耦合移動邊界法發展及其於山崩海嘯之研究
(Developing a Two-way Coupled Moving Solid Method for Solving Landslide Generated Tsunamis)

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摘要(中)

山崩引發海嘯是自然界最嚴重的災害之一，然而在數值模擬上，由於固體邊界與自由液面交互之影響，使得求解此問題存在著一定的困難度。Liu et al (2005) 展示水面上與水面下滑落巨石之實驗與數值模擬，研究中發展了單向耦合的移動固體法，但該移動固體法必須事先給定山崩塊體滑落之路徑，故其應用範圍因而受限。本研究發展雙向耦合移動邊界法，採用離散元素法計算由求解Navier-Stokes方程式給予固體表面壓力預測其運動行為，以流體體積法追蹤自由液面，並以投影法計算壓力與速度場。以移動邊界法為橋樑，結合雙向耦合離散元素法與流體體積法，藉由移動固體法，我們將可描述固體的運動路徑。
　　本研究利用山崩引發海嘯之實驗數據來驗證雙向耦合模式，結果顯示數值計算之固體路徑與實驗紀錄相當吻合。模擬結果顯示，當山崩塊體密度小於2100 kg/m3時，塊體之滑落運動受水體壓力有明顯的影響。一般而言,塊體在空氣中運動時，呈現正加速度之移動;而塊體在剛進入水面時，則呈現負加速度之運動。數值模擬發現,塊體在下潛至2倍塊體尺度後，將達終端速度。當塊體密度大於3400 kg/m3後，負加速度的表現極不明顯，並在下潛至0.5倍塊體尺度後，產生終端速度。此外,本研究加寬實驗渠道，以了解渠寬對於塊體移動之影響。
　　本研究進一步模擬水中漂浮之固體運動，密度分別為600 kg/m3到800 kg/m3之固體,發現該運動具有複雜之六個自由度，將其結果與理論解比較，以驗證流固耦合模式之準確度，並提供未來於港口沉箱作業應用之參考。

摘要(英)

The landslide generated tsunami is one of the most devastating nature hazards. Because both the moving solid boundary and free-surface are involved and coupled together, it makes numerical simulation a difficult task. Liu et al. (2005) performed laboratory experiment and numerical simulation of a sub-aerial and sub-merged rock slide. A one-way coupled moving solid method was developed and adopted in their study. However, the rock trajectory was required to perform the one-way coupled moving solid method which greatly limited the implementations. In this study, a two-way coupled moving solid algorithm is developed. The sophisticated discrete element method (DEM) model is utilized to predict the solid motion based on the surface pressure obtained from solving the Navier-Stokes equations. The free-surface kinematic is tracked by the volume-of-fluid (VOF) method. The modified projection method is used to decouple and solve the pressure and velocity field. The two-way coupled moving solid method is developed to bridge the DEM model and VOF model. With this newly developed moving-solid method, the trajectory of the solid motion is no longer needed to be prescribed.
The two-way coupled model is then validated by the experiment of landslide tsunamis. The simulation result shows that the predicted solid trajectory is very close to the experimental result. As the solid density is less than 2100 kg/m3, the solid sliding motion is greatly influenced by the water pressure. An acceleration of the solid motion is captured before the solid reaches the free-surface. When the solid is entering the water, the deceleration is observed. The solid then reaches the terminal velocity after diving into a depth twice of the solid height. However, this deceleration will not be observed if the solid density is higher than 3400 kg/m3. The deceleration ceases and the solid motion soon reaches the terminal velocity after a depth of half of the solid height. The effect of the width of channel is also studied to identify the wave reflection from the side walls.
In this study, we further simulate the motion of a floating cube with density from 600 kg/m3 to 800 kg/m3. The floating motion has 6 DOF (degrees of freedom) which is very sensitive to the accuracy of the coupling. The results are compared with the analytical solution. This simulation could be used to predict the caisson work in the future.

關鍵字(中)

★ 山崩海嘯
★ 流體體積法
★ 移動固體法
★ 離散元素法
★ 浮動塊體

關鍵字(英)

★ Volume of Fluid (VOF)
★ Discrete Element Method (DEM)
★ Landslide Tsunami
★ Moving solid algorithm
★ Floating cube

論文目次

摘要 I
ABSTRACT III
誌謝 V
Table of Contents VI
List of Tables VIII
List of Figures IX
Chapter 1 Introduction 1
1-1 Motivation 1
1-2 Scope of Present Study 3
Chapter 2 Literature Review 4
2-1 Review of Flow with Free-Surface 4
2-2 Review of Internal Irregular Boundaries 6
2-3 Review of Solid Mechanics 7
2-4 Review of Solid Fluid Coupling 8
2-4-1 One-Way Coupling 8
2-4-2 Two-Way Coupling 9
Chapter 3 Algorithm 11
3-1 Fluid Model 11
3-1-1 Governing Equations of Fluids 11
3-1-2 Volume of fluid method for multi-phase flow 13
3-1-3 Finite Volume Method 18
3-1-4 Projection Method 20
3-1-5 Partial-Cell Method 22
3-1-6 Moving-Solid Algorithm 23
3-2 Motion Analysis of Discrete Bodies 24
3-2-1 Governing Equation of Solid Motion 24
3-2-2 Pressure Force on the Solid Bodies 28
3-2-3 Pressure Interpolation 28
3-2-4 Displacement of Bodies 29
3-3 Computational Cycle 35
Chapter 4 Landslide Tsunami Simulation 37
4.1 Setup 37
4.2 Result and Discussion 45
Chapter 5 Floating Cube Simulation 58
5.1 Setup 58
5.2 Result and Discussion 61
Chapter 6 Conclusions and Future Works 67
References 68

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指導教授

吳祚任(Tso-ren Wu)

審核日期

2009-7-24

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