2017年6月，格陵蘭島西岸之卡拉特峽灣（Karrat Fjord）發生山崩海嘯事件，估計體積約4500萬立方公尺之山崩滑落，引發之海嘯侵襲南方之Nuugaatsiaq漁村，造成結構物破壞以及數人死亡。相較於海底地震引發之海嘯，山崩海嘯具有較強烈之垂直擾動，且往往伴隨劇烈之碎波，必須以三維數值方法獲得更精確之模擬。

　　台灣為較易受海嘯攻擊之海島，亦有十數筆歷史海嘯以及古海嘯紀錄（Wu, 2013），然而海嘯石為研究古海嘯之重要地質線索，由海嘯石最終所停留之位置，有機會一窺當時海嘯來臨時之波高與流速，並釐清動力來源，如海嘯或颱風巨浪。此外，台灣屏東九鵬已發現三顆海嘯石（Matta et al., 2013），透過分析其動力機制，有機會還原古海嘯之情境。

　　然而，山崩海嘯與海嘯石之運動皆關係到雙相流流體力學與固體力學之耦合，為此，本研究開發嶄新之剛性流體法（Rigid-Fluid Method, RFM），求解三維不可壓縮流之Navier-Stokes方程式，以流體體積法（VOF）搭配PLIC法描述自由液面，並應用離散元素法（DEM），透過收集網格中之壓力及剪力，計算固體之移動及旋轉。本文使用RFM法，對半圓球山崩海嘯實驗、格陵蘭山崩海嘯以及九鵬海嘯石，進行一系列之模擬以及分析，獲得非常準確之驗證，以及符合文獻描述之模擬結果。

　　本研究結果顯示，半圓球山崩之側向流速將逐漸增大，且塊體浸沒深度達2.5倍半圓球直徑後，已難影響上層之流場。將模擬之尺度放大後，模擬結果之參數皆符合福祿數相似時之倍數關係。格陵蘭山崩模擬之溯上高度可達90公尺，符合Nature News報導之數據。在1:5坡度條件下，海嘯石搬運之條件為至少1.5倍直徑波高之湧潮，以及至少 √2gh 之流速。

　　In June, 2017, a landslide-tsunami event took place at Karrat fjord, locating at the west coast of Greenland. The volume of the landslide is approximately 45 million cubic meter. As the result, the tsunami brought destructions and several casualties to a fishing village at Nuugaatsiaq. In order to investigate further physical properties of this event, we must not ignore the high nonlinearity of breaking waves induced by great vertical vibration. Therefore, a 3D numerical analysis is taken to obtain accurately reproduce the scenario.

　　Rigid-Fluid Method (RFM), which solves the Navier-Stokes equation for three-dimensional incompressible flow, is developed to calculate the movement and rotation of a moving solid. With the data of the pressure and shear stress in each grid collected by Discrete Element Method (DEM), the moving solid is granted to be involved in the simulation; while the free surface is reconstructed by Piecewise Linear Interface Calculation (PLIC).

　　A series of simulations and analyses of the Greenland Tsunami, the Jiu Peng tsunami boulders, and a hemisphere landslide tsunami experiment have been performed. The numerical results, which concur with the literature records, indicate the correctness of this method even a moving solid is included.

論文指導教授推薦書 iii
論文口試委員審定書 iv
摘要 v
Abstract vii
誌謝 viii
目錄 x
圖目錄 xiii
表目錄 xvii
第一章　緒論 1
1-1　研究動機 1
1-2　研究方法 4
1-3　本文架構 6
第二章　文獻回顧 8
2-1　山崩海嘯文獻回顧 8
2-2　海嘯石文獻回顧 12
2-3　流固耦合方法回顧 15
2-4　移動固體法開發演進 17
第三章　模式介紹與數值方法 19
3-1　控制方程式（Governing Equation） 20
3-2　流體體積法與PLIC法（Piecewise Linear Interface Construction） 22
3-3　有限體積法（Finite Volume Method, FVM） 25
3-4　部分網格法（Partial Cell Treatment, PCT） 27
3-5　大渦模擬法（Large Eddy Simulation, LES） 28
3-6　卵形顆粒描述法（Egg-Shaped Particles Description） 31
3-7　離散元素法（Discrete Element Method, DEM） 35
3-8　投影法（Projection Method） 37
3-9　RFM法（Rigid-Fluid Method） 39
第四章　模式驗證 42
4-1　卡門渦街案例數值設置 43
4-2　卡門渦街案例模擬結果 45
4-3　圓球入水案例實驗及數值設置 51
4-4　圓球入水案例模擬結果 54
第五章　山崩海嘯案例之模擬結果與分析 73
5-1　半圓球山崩案例之實驗與模擬設置 76
5-2　半圓球山崩案例模擬結果 80
5-3　大尺度之半圓球山崩案例模擬 111
5-4　2017格陵蘭山崩海嘯案例模擬設置 123
5-5　格陵蘭山崩海嘯案例模擬結果 129
第六章　九鵬海嘯石案例之模擬結果與討論 163
6-1　九鵬海嘯石案例之模擬設置 166
6-2　九鵬海嘯石案例模擬結果 168
第七章　結論與建議 182
7-1　模式驗證 182
7-2　山崩海嘯案例之模擬結論 183
7-3　九鵬海嘯石案例之模擬結論 184
7-4　建議 184
參考文獻 185
論文口試書面答覆表 194

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