本模式以無網格方法所建立之三維模式，求解拉普拉斯方程式(Laplace equation)，模擬孤立波與規則波。本數值模式主要架構為Wu and Tsay(2012)和Wu et al.(2014)發展之二維無網格模式，其特色是以局部近似(Local approximation)的方法求解，此舉加快了其運算的效率。後經本研究修改其造波邊界及增至三維模式，而進行模試驗證。
本研究之驗證分兩部分，分別為Beji and Battjes(1994)規則波通過潛堤之試驗和Chambarel et al.(2009)驗證孤立波撞擊直立壁之試驗。從前者的驗證結果，不僅與試驗結果吻合，更在計算效率上明顯比黃大祐(2012)無網格法之結果更好，更進一步觀察全域之調和波高圖，討論其規則波在通過潛堤時之能量傳遞之情形；後者模擬結果與Chambarel et al.(2009)之邊界積分法模擬結果比較，也有不錯的吻合度。
但波浪與結構物之作用為三維問題，並且在二維模式下，波浪與結構物之交互作用所產生的繞射與折射之現象是無法觀察得到，因此將二維模式擴展至三維模式並應於Mo(2010)的孤立波通過圓柱之問題及Whalin(1971)的規則波通過變水深底床的問題，為本研究之核心問題。

The purpose of the present study is to develop a three-dimensional, fully nonlinear wave model using meshless method based on Wu and Tsay (2012). This meshless method utilizes local approximation to solve the governing equations which is more efficient than that used RBF-collocation counterpart. Furthermore, due to its Lagrangian description of flow motion, this meshless method is powerful in dealing with moving boundaries such as free surface, landslide and wave-maker boundaries.
To validate the developed three-dimensional model, both two-dimensional and three-dimensional experiments were tested and compared. Particularly, for two-dimensional cases, regular waves propagation over a submerged trapezoidal breakwater (Beji and Battjes (1994)) and a solitary wave interaction with vertical wall (Chambarel et al. (2009)) were conducted. The comparisons show this model can efficiently and accurately capture the associated hydrodynamic processes. The model is then applied to three-dimensional experiments including a solitary wave interacting with a circular cylinder (Mo, 2010) and regular waves pass an uneven bottom (Whalin, 1970, 1971). The present simulated results agree the measured data pretty well, indicating that the present model can well capture important phenomenon such as wave refraction and diffraction.

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