利用修正有限配點無網格法於水波散射問題

Applications of Modified Finite Point Method to Water-wave Scattering

楊淳文(Chun-Wen Yang)

指導教授 ： 蔡丁貴

國立臺灣大學/工學院/土木工程學研究所/碩士(2012年)

https://doi.org/10.6342/NTU.2012.01568

摘要

摘要
本研究應用最近發展之數值方法－修正有限配點法，建立水波散射之數值模式，探討水波遇到結構物或島嶼，發生繞射、反射及折射之後的振幅、波高及速度場等，研究結構物對於水波的影響。
應用本模式計算入射水波受到圓柱、拋物線型圓島作用後，產生散射、繞射、折射的問題，初步得到結果良好；其次，本模式不只能夠順利求得速度勢能與波高，並且能直接準確求出速度勢能之偏導數而決定流場。
本模式應用於港池共振方面之問題，模擬不同週期之波浪於狹長港灣情形，分別計算港灣內的水波振幅，及其共振之振幅放大係數，初步結果亦良好，證明本模式亦可應用於狹長港池共振問題之研究。
本研究以數值計算結果與解析解比較，結果良好，初步證明以修正有限配點法及緩坡方程式(Mild slope equation)，所建立之水波散射數值模式可應用於研究海岸波浪反射、折射、繞射、散射及共振問題。

關鍵字

修正有限配點法 ； 無網格數值方法 ； 緩坡方程式 ； 水波散射 ； 港池共振

並列摘要

ABSTRACT
In this research, The Modified Finite Point collocation Method (MFPM) is applied to　establish a numerical model of water wave, describing the phenomenon of 　combined reflection, diffraction, and refraction of water wave.
Cases of water surface waves affected by cylinder with constant depths and parabolic-varying depths have been successfully verified by comparing present numerical results with analytical solutions. It is not only the wave amplitude can be obtained, but also the velocity field can be derived directly and accurately.
In the case of harbor oscillation, different frequencies of incident waves are calculated in the narrow harbor of constant depth. Numerical solutions in the harbor basin is shown to agree very well with the analytical solutions (Mei, 1983).
It is concluded that a numerical model by employing MFPM and the mild slope equation has been successfully developed. Present numerical model can accurately and efficiently be applied to simulate water-wave scattering problems.

並列關鍵字

Modified Finite Point Method (MFPM) ； Meshless method ； Mild-slope equation ； wave scattering ； harbor oscillation

參考文獻

19. 吳智文，“無網格數值方法應用於水面波散射之研究”，國立台灣大學土木工程學研究所碩士論文，2008。

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