請用此 Handle URI 來引用此文件:
http://tdr.lib.ntu.edu.tw/jspui/handle/123456789/27136
標題: | 無網格數值方法應用於水面波散射之研究 Applications of Meshless Methods to Water-wave Scattering |
作者: | Zhi-Wen Wu 吳智文 |
指導教授: | 蔡丁貴(Ting-Kuei Tsay) |
關鍵字: | 無網格數值方法,散射,堪薩氏法,高斯輻狀基底函數,緩坡方程式, numerical meshless method,scattering,Kansa’s method,Gaussian radial basis function,mild-slope equation, |
出版年 : | 2008 |
學位: | 碩士 |
摘要: | 本論文的主旨是用無網格數值方法來探討水波散射的數值計算問題。無網格數值方法有3種型態,本研究是參考Multiquadratics(MQ)或Kansa’s method (1990),但選取不同於MQ的高斯輻狀基底函數( Gaussian radial basis function)來求解。目的在於建立一個數值計算方法,以克服以往傳統數值方法處理波場中速度問題的困難,另一個優點是可避免建置數值網格繁瑣的前置工作。本文以基本的水波散射問題,假設波場為非壓縮、無黏性流之非旋流,則速度勢則為滿足平面二維的緩坡方程式。討論單頻前進波在受到等水深圓柱及拋物線型水深圓島產生散射波場的兩個例子探討無網格數值方法對此類問題的實用性,利用本研究建立之模式所計算出水波的振幅、相位及徑向速度及切線速度等數值結果,將其與MacCormick 和Fuch(1954)所推導之等水深圓柱解析解以及Homma(1950)所推導之長波受拋物線型圓島散射之解析解做比較。由計算結果的準確性證實本文所建立數值模式是一個可以有效計算水波散射速度場的方法。 The main objective of this thesis is to extend application of a numerical meshless method to water wave scattering problems. There are three kinds of meshless methods. A method similar to the Multiquadratics (MQ) or Kansa’s method is employed in this research. Gaussian radial basis function different from those of the MQ is chosen to solve water wave scattering problems.It is intended to overcome difficulty in obtaining velocity field of water wave problems when traditional numerical methods are used. Another obvious advantage of numerical meshless methods is the avoidance of tedious grid generation for numerical computations.In this thesis,two water wave scattering problems are investigated. Monochromatic, progressive waves are scattered by a cylinder with constant water depths and a island with a parabolic shoal are used for testing the meshless method.Assuming flow field is irrotational for inviscid fluids,velocity potential satisfies the two- dimensional mild-slope equation. Numerical solutions of wave amplitude, phase,radial velocity,and angular velocity are calculated and compared with analytical solutions of waves scattered by a cylinder with constant water depths (MacCormick and Fuch,1954) and a island with a shoal (Homma,1950).Very good agreement demonstrates that present numerical meshless method is applicable to water wave scattering problems. |
URI: | http://tdr.lib.ntu.edu.tw/jspui/handle/123456789/27136 |
全文授權: | 有償授權 |
顯示於系所單位: | 土木工程學系 |
文件中的檔案:
檔案 | 大小 | 格式 | |
---|---|---|---|
ntu-97-1.pdf 目前未授權公開取用 | 3.57 MB | Adobe PDF |
系統中的文件,除了特別指名其著作權條款之外,均受到著作權保護,並且保留所有的權利。