在工程上經常使用淺水波方程式來模擬淺水波問題。在自然界的水體在水平方
向的運動較垂直方向更為重要且實務上較為關注水平方向流動的趨勢，因此將複雜
的三維問題簡化為二維，並且假設壓力在垂直方向為線性分布(即不考慮波浪所引致
的壓力變化，僅考慮水體所產生的靜水壓) 可推得淺水波方程式。
若上述之假設符合實際之物理現象，以淺水波方程式為控制方程式輔並以數值
方法建立一套運算模式，運算所得之結果應當貼近實驗結果與數學理論；但卻發現
以淺水波方程式模擬孤立波於水平底床的傳遞，會導致孤立波於傳遞過程出現波形
向前傾倒與不對稱的現象，而且在傳遞中孤立波的波峰亦會有逐步遞減的情況，與
數學上所描述的對稱波形並不相同。
本研究以Wu et al. (2021) 的研究作為基礎，以非靜水壓淺水波方程式(nonhydrostatic
shallow water equations) 為控制方程式並基於無網格數值方法(meshless
method) 為數值方法，再將數值模式加入乾溼點演算法(wet-dry algorithm) 使得模式
得以模擬溯升的物理現象，並以四個案例來驗證當前模型之結果。
案例一，使孤立波通過水平底床來驗證模型的穩定性，目的在於觀察孤立波的
波形有無傾倒、波峰有無下滑，並將模式的結果與Goring and Raichlen (1980) 解析解
進行比對。
案例二，將從邊界生成規則波，並參考Madsen (1971) 所推得規則波的邊界速度
帶入本模式左側之造波邊界，將所得自由液面結果與Madsen (1971) 實驗結果與Wu et
al. (2021) 的數值結果進行比對。
案例三，參考Grilli (1997) 的地形配置使孤立波通過地形變化，並將本模式計算
所得之自由液面結果與Grilli (1997) 的波高計資料做驗證。
案例四，使孤立波溯升於一陡峭斜坡(1:2.75)，將自由液面時序資料與Zelt
(1991) 的波高計結果作驗證，並將本模式的溯升過程和實驗比對。

This paper developed a numerical method based on the non-hydrostatic shallow-water equation to simulate several wave problems. In previous studies, the hydrostatic assumption was broadly applied to the shallow-water-equation, but the results were usually not satisfying. The reason for the errors is that the dispersion terms are ignored in the equations, so it induced the phenomenon of wave inclined or asymmetry. Therefore, this study divided the pressure into hydrostatic and non-hydrostatic terms to optimize the simulation. In addition, this research applied the weighted-least-squares meshless method to approximate the spatial derivatives. To validate the stability and accuracy of the present model, four benchmark problems are demonstrated in this study. The computed results can not only coincide with the experimental data but also save a lot of computation time.

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