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研究生： 林宗翰
Lin, Zhong-Han
論文名稱： 應用LRCM處理波浪輻射邊界問題
Applying LRCM to Deal with Radiation Boundary Condition of Wave Problems
指導教授： 許泰文
Hsu, Tai-Wen
學位類別： 碩士
Master
系所名稱： 工學院 - 水利及海洋工程學系
Department of Hydraulic & Ocean Engineering
論文出版年： 2014
畢業學年度： 102
語文別： 英文
論文頁數： 91
中文關鍵詞： 輻射邊界 、緩坡方程式 、無網格法 、區域徑向基底函數配點法
外文關鍵詞： Radiation boundary condition, Mild-slope equation, Mesh-less numerical method, Local radial basis function collocation method
相關次數： 點閱：138  下載：3 
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    • 本文利用區域徑向基底函數配點法(LRCM)解析橢圓型態之緩坡方程式(MSE)，用以模擬波浪大角度入射時之波場。本文使用之LRCM為無網格法，相較於傳統的數值方法，在高階輻射邊界的處理上較為簡單。本文將輻射邊界展開至三階，以處理波浪斜向入射之問題。此外，文中以不同的障礙物進行驗證計算，包括波浪通過垂直圓柱和淺水長波通過拋物線型潛灘，並與前人理論所推導之解析解進行比較，其結果顯示模式之預測值與解析解相互符合，特別是在波浪大角度入射的情況下，使用高階輻射邊界的結果與解析解呈現良好之一致性。

    The local radial basis function collocation method (LRCM) uses a multiquadric type radial basis function to simulate water wave propagation with oblique incidence. LRCM is a mesh-less numerical method and its applications to the high-order radiation boundary conditions are much simpler compared with the traditional numerical methods. In this study, the mild-slope equation (MSE) is used and the radiation boundary condition is expanded to the third-order approximation for solving the MSE. Two typical numerical cases, waves scattering around a vertical cylinder and shallow water waves propagating over a submerged shoal, are used to validate the present model. The numerical results for the third-order radiation boundary condition are in a better agreement with than those of the first-order and second-order radiation boundary conditions for large incident angle.

    摘要 I Abstract II 誌謝 III Table of Contents IV List of Figures VI List of Tables XI List of Acronyms XII List of Symbols XIII Chapter 1 Introduction 1 1.1 Problem Statement 1 1.2 Motivation 4 1.3 Literature Review 6 1.4 Contents of Thesis 10 Chapter 2 Numerical Model 11 2.1 Governing Equation 11 2.2 Radiation Boundary Conditions (RBCs) 12 Chapter 3 Local RBF Collocation Method 19 3.1 Radial Basis Function (RBF) 19 3.2 Local RBF Collocation Method (LRCM) 20 3.3 Operator on RBF 24 3.4 Example for LRCM 26 Chapter 4 Numerical Results 31 4.1 Waves scattering around a vertical cylinder 32 4.2 Shallow water waves propagating over a submerged shoal 50 Chapter 5 Conclusions 67 5.1 Conclusions 67 5.2 Suggestions 68 References 69 Appendix A. Derivation of MSE 73 Appendix B. Padé Approximation 77 Appendix C. Analytical solutions of waves scattering around a vertical cylinder 81 Appendix D. Analytical solutions of shallow water waves over a circular shoal 83 Appendix E. General solution for shallow water waves over a varying depth 87

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