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.

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