修正有限配點法應用於水域潮汐數值模擬之研究

Abstract

本研究探討在地球自轉的效應下，潮波遇到結構物或島嶼，發生繞射、反射及折射之後的振幅、相位及速度場的變化情形，以期能更準確的模擬自然現象。本研究最主要的目標為以下兩點，第一，針對數值計算方法中的參數選擇進行討論；另一個是利用本數值計算方法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。 本研究應用修正有限配點法，根據Tasy （1991）推導建立緩坡方程式（mild-slope equation）之數值模式，且利用本模式計算入射水波受到等水深之圓柱及拋物線變化水深之圓島作用後，產生散射、繞射、折射的問題。 本文將數值計算結果與解析解比較，證明利用修正有限配點法所建立之潮波散射數值模式，可應用於研究海岸波浪之問題。並針對數值模式中的參數進行討論，推判本模式計算可達到穩定且準確目標。

When tide waves hits the island or construction, they reflect, diffract, and refract. This research studies the distribution of wave amplitude, and phase and velocity field of tidal waves including the effects of the Earth’s rotation. This research aims are two folds. One is to find a selection rule of the parameters in the chosen numerical method. The other one is the take advantage of the chores numerical method to determine tidal velocity field, after amplitude and phase of tidal waves are found. In this research, the modified finite point collocation method (MFPM) is applied to establish a numerical model of tide flow hased on an extended mild-slope equation（1991）, describing the phenomenon of combined reflection, diffraction and refraction of tide flow. Compare numerical model with analytic solution, it is concluded that a numerical model employed by MFPM can solve the problem of combined wave refraction and diffraction. Besides, this research has developed an rule for feller systematical selection of the parameter in the present numerical method, in order to achieve a accurate result.