Meshless Implementation on Numerical Model Development of Boussinesq Equation

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Project title

Code/計畫編號

MOST105-2221-E019-039-MY3

Translated Name/計畫中文名

以無網格建置布氏方程式數值模式

Project Coordinator/計畫主持人

Tai-Wen Hsu

Co-Investigator(s)/共同執行人

蔡加正

Department/Unit

Research Center of Ocean Energy and Strategies

Website

https://www.grb.gov.tw/search/planDetail?id=11903391

Year

2016

Start date/計畫起

01-08-2016

Expected Completion/計畫迄

01-07-2017

Bugetid/研究經費

1026千元

數值計算上無網格方法的特點是無論在計算域中或是邊界上皆不需要配置網格，也不依靠建構網格點之間的關係作計算。本計晝將應用無網格數值法的區域徑向基底函數配點法，此方法應用在許多工程問題上，例如熱傳、非線性Burgers方程式、淺水波方程式、Stoke流體、電磁問題等。局部徑向基函數配點法(local radial basis function collocation method, LRBFCM)主要的概念是只有在整個區域中相鄰節點相關連的内插函數值，與密集矩陣相比之下，此方法所使用的稀疏矩陣更能達到計算的效率。在布斯尼斯克方程式（Boussinesq Equation)理論的推導中，根據不同水平流速的描述，以及高階量的取決均會得到不同形式的布斯尼斯克方程式，然而典型的布斯尼斯克方程式描述非線性較強烈之波浪變形時，該存在之弱頻散性質必會造成其波速上的誤差，故此方程式僅適用於較小的相對水深。本計晝第一年度將利用高階完全非線性布斯尼斯克模式搭配能處理高階非線性邊界條件之區域徑向基底函數配點法來處理波浪變形的問題，如此大角度平面波場或者是複雜場域計算能藉由區域化過程使密矩陣系統轉化為稀疏矩陣系統，並獲得整體計算效率上相當程度之改善。第二年度則是以布拉格反射為例進行模式驗證，並探討高階輻射邊界條件的改善與海綿層阻尼消波參數的調教。第三年將以標準JONSWAP波譜為基礎探討不同類型珊瑚群礁地形之波能變化。最後，本計晝研究結果將展現於國際期刊上。 Meshless methods do not require numerical grids in the computing domain or on the boundary when solving boundary problems. In this project we consider a meshless numerical method, called the local radial basis function collocation method (LRBFCM). The LRBFCM has been applied for solving many engineering problems, e.g., heat transfer, nonlinear Burger's equation, shallow water equation , Stoke fluid, electromagnetic field, and so on. The main concept of the LRBFCM is the interpolation function values which is only associated with the neighboring nodes in the entire domain. In contrast to the fully dense matrices with the global methods, the localized approach results in sparse matrices which promotes the computation efficiency. In the theory of Boussinesq equation (BE), different types of BE is relevant to different horizontal velocities and higher order terms. However, the classic BE cannot simulate a highly nonlinear wave deformation and there are some errors of the wave velocity. All the reasons are arisen from the character of weak dispersion relation. In the first year of this project, a fully nonlinear Boussinesq model and the LRBFCM are decoupled to simulate wave deformations. Furthermore, the computing efficiency of a complex domain calculation and problems of wide range incidence of the plane wave has been improved by a simplified process of computing matrix system. In second year, a verification of the model will be implemented by a case of Bragg resonance and the problem of harbor resonance. An improvement of the radiation boundary condition will be explored and the damping parameter of wave dissipation will be adjusted as well. In the last year, we make our model apply in some case of the fringing reefs.. Variations of wave energy will be explored when waves generated by JONSWAP spectra travel over a fringing reef. All research results of this project will be published on the international journals.

Keyword(s)

無網格數值方法
布斯尼斯克方程式
區域徑向基底函數配點法
阻尼消波
布拉格反射
珊瑚群礁
Boussinesq equation
Meshless method
Local radial basis function collocation method
fringing reef

DSpace CRIS

Meshless Implementation on Numerical Model Development of Boussinesq Equation

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