本研究建立含虛擬時間項之透水緩坡方程式，用以模擬波浪通過潛沒式透水結構物之變形效應，稱之為 FTIMEMSE (Fictitious-Time Integration Method Extended Mild-Slope Equation) 模式。文中以線性波理論為基礎，對水深積分將三維問題簡化為二維平面問題，重新推導含有陡變透水底床效應之緩坡方程式 (Mild-Slope Equation，MSE)，使控制方程式可以描述陡變地形之透水介質，並使用虛擬時間積分法 (Fictitious Time Integration Method，FTIM) 於控制方程式中，使模式具有抗雜訊 (noise) 的能力。
本研究提出改良型輻射邊界條件 (Improved radiation boundary condition, IRBC) 處理複雜側向邊界之波浪反射和大角度入射的問題，使模式更能適切描述波浪通過複雜透水地形之變形。對波浪大角度入射邊界的問題，本研究利用廣義型 Padé [2,2] 近似 (generalized Padé [2,2] approximation) 展開邊界條件，用以消除計算領域波能之疊加，同時提高模式估算精度。
本研究數值模擬結果經與前人試驗及理論解析結果比較，發現模式模擬與試驗及理論結果呈現合理的一致性。文中並進一步分析本研究側向邊界近似展開對計算精度之提昇及其限制。本研究亦於大型平面水槽進行波浪斜向通過斜坡上潛沒式透水與不透水圓柱之試驗，用以校驗數值模式之適用範圍，同時瞭解波浪通過透水結構物能量消散的機制。
本研究進行模式之參數分析，以及探討高階陡變透項在不同水深變化下的特性分析，從分析結果探討陡變項和模式參數之敏感度。本研究同時進行模式抗雜訊的特性分析，從分析解果證實本研究模式除了可以合理地模擬波浪通過各式結構物的的變形效應外，亦可有效地抑止輸入源所導致的誤差累加現象。

An integrated numerical model using fictitious time integration method (FTIM) was developed to simulate wave transformation over porous structures across the surf zone including wave shoaling, refraction, diffraction, reflection, breaking and energy dissipation. Based on linear wave theory, the Mild-Slope Equation (MSE) with higher-order rapidly changed porous bed trems was drived. The FTIM converts the elliptic type of MSE into a FTIM extended MSE (FTIMEMSE) which is capable of decreasing the noise due to in correct input resources.
In this study, the Parabolic Mild-Slope Equation (PMSE) model that developed by Hsu et al. (2008a) was employed to the Improved Radiation Boundary Condition (IRBC) in present model. The reflected waves at the boundary caused by verying water depth are separated from scattering and incident waves in this model. This IRBC makes reflected waves go out from the computational domain. Numerical results show that the model is capable of describing waves propagating over porous structures resting on rapidly changed bottom configuration. The Padé [2,2] approximation is also used to enable a more accurate description of combined wave refraction, diffraction and reflection with large angle indence.
The model is validated through experimental data and analytical soluctions for wave propagating over permeable structures. The results show that the model predictions are in good agreements. A large-scale experiment was also conducted in a three-dimensional wave basin to generate waves travelling over a permeable submerged circular pile placed on a sloping bottom. The comparison of planary wave height variations demonstrates that the present model is able to produce wave transformation ove porous structure including wave breaking ans energy dissipation.
Sensibility analysis of influence parameters such as the porocity , the linear friction , relative porous depth and higher-order bottom slope and curvatures terms was conducted. The numerical results suggest a proper selection is required for practical application because different results of parameters could yield different wave patterns. The tested cases also investity the applicability of FTIM used in the model. Typical examples for waves propagating over permeable or impermeable elliptic shoal rest on a horizontal and sloping bottom are also presented. It is concluded that the FTIMEMSE is robust in the numerical stability and capable of tolersting the noise of the measurement.

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