本研究以橢圓型態之緩坡方程式(Mild slope equation)為基礎,應用無網格數值計算法中的修正有限配點法(Modified finite point method, MFPM)模擬近岸波場。 此方法乃是以局部多項式為基底配合最小二乘法近似欲求函數,優點在於給定一懲罰性權重使得計算格點更加滿足控制方程式及邊界條件,大大地提昇計算後之函數值的準確度。 本研究目的為準確描述能量消散後之碎波點位置。控制方程式於緩坡方程式中加入能量消散項,並將碎波能量消散項與碎波指標納入緩坡方程式中以描述水波反射、折射、繞射、淺化、碎波及能量消散等波浪變形之物理現象。本文數值計算結果與理論值及其他實驗量測值比較,得到良好的結果。配合近岸流及地形變化模式,往後將能夠完整地描述近岸海域之水動力系統及漂沙運轉特性以提供實際工程設計上之依據。
In this thesis, a numerical model based on elliptic mild-slope equation is developed by using a special mesh-less numerical methods, namely, Modified Finite Point Method (MFPM) to simulate nearshore wave field. Present methoduseaslocal polynomial function to formulateand to be solved with moving least square (MLS) approach. Computational points satisfy governing equation and boundary conditions by giving a weighting factor. Accuracy of numerical computations is improved. The purpose of this research is to simulate breaking processes with energy dissipation term followed a rule obtained by experimental results. It is intended tosimulate the physical phenomena of water wave,transformation in the coastal areas, withreflection, refraction, diffraction, shoaling, and breaking. Present numerical results are compared with theoretical results, and experiment at measurements. Present model will be extended as a basis for further development of numerical models of nearshore currents and coastal sediments.