Simulation of Water Waves by Higher Order Mild-Slope Equation (III)

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Project title

Code/計畫編號

NSC96-2221-E006-061-

Translated Name/計畫中文名

近岸波場變形之研究---以高階緩坡方程式模擬波浪之變形(III)

Project Coordinator/計畫主持人

Tai-Wen Hsu

Co-Investigator(s)/共同執行人

許泰文

Website

https://www.grb.gov.tw/search/planDetail?id=1443165

Year

2008

Start date/計畫起

01-08-2007

Expected Completion/計畫迄

01-07-2008

Bugetid/研究經費

762千元

波浪從深海傳遞至淺海，由於地形水深的變化或結構物之阻擋，而發生波浪變形。波浪變形包括淺化、折射、繞射、反射、碎波與能量消散，這些變形通常共存發生。本計畫擬推導並建立高階緩坡方程式，並利用交錯方向隱式法 (Alternative Directional Implicit, ADI) 來建立波場模式，以模擬波浪變形效應。第一年主要由 Biesel (1952)求解滿足斜坡底床邊界條件之水深函數，並重新推導新的高階緩坡方程式，以提高數值計算精度，並掌握斜坡底床的波動現象，同時並與水工模型試驗相互驗證。第二年考慮非線性緩坡方程式推導至較高階的項，並使用交錯方向隱式法進行計算，本計畫將輻射邊界條件利用Padé [2,2] 之階數展開邊界條件，使大角度入射之波浪在計算領域的邊界上反射波能大幅消減，加速數值疊代之收斂條件，同時與水工模型試驗之結果相互驗證。第三年則延續前兩年之結果，應用前二年之成果，將高階緩坡方程式應用於不規則波之變形。將Hsu等人 (2002) 的理論應用於Hsu 等人 (2004) 所發展的EEMSE模式，並考慮陡變地形，同時並與水工模型試驗結果相互驗證，使緩坡方程式的應用更為廣泛。 In this study, a nonlinear mild-slope equation is derived and estimated by a alternative directional implicit method to simulate wave transformation, including shoaling, refraction, diffraction, reflection, wave breaking and energy dissipation from deep water to shallow water. We introduce the new depth function of the bottom slope addressed by Biesel (1952) to propose a new nonlinear mild-slope equation in the first year. In the second year, the traditional radiation boundary conditions are improved by using Pade’[2,2] approximation which can be used to simulate wave propagation at very wide angles. The method will efficiently reduce the reflected waves going back into the computational domain to achieve a higher resolution of numerical simulation. We use the nonlinear mild-slope equation to calculate the wave fields of irregular waves in the last year. The validity of the model is examined through comparisons with experiments.

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Simulation of Water Waves by Higher Order Mild-Slope Equation (III)

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