Development and Application of the Three-Dimensional Mesh-Free Numerical Model for Nonlinear Water Waves

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Project title

Code/計畫編號

MOST103-2221-E415-030

Translated Name/計畫中文名

非線性水波三維無網格數值模式之發展與應用

Project Coordinator/計畫主持人

Nan-Jing Wu

Funding Organization/主管機關

National Science and Technology Council

Department/Unit

Tainan Hydrotech Laboratory,NCKU

Website

https://www.grb.gov.tw/search/planDetail?id=8351581

Year

2014

Start date/計畫起

01-08-2014

Expected Completion/計畫迄

31-07-2015

Bugetid/研究經費

770千元

ResearchField/研究領域

土木水利工程
海洋科學

本計畫期程為二年，將建立一套能夠模擬三維非線性水波之無網格數值模式。本模式採用之演算法，係 Wu and Chang (2011)提出 Lagrangian 觀點可預測水面質點軌跡之方法。在每個時間步求解一次 Laplace 方程式，進而求出流體質點的速度，提供給下個時間步預測流體質點位置之用。求解 Laplace 方程式之數值方法，則為 Wu and Tsay(2013)提出之局部多項式有限配點法(Local Polynomial Collocation Method)。這個數值方法具有產生稀疏矩陣的特性，將適用於大尺度之實際問題。關於 Wu and Chang (2011)演算法及 Wu and Tsay (2013)數值方法之結合，目前已有二維之初步成果，Wu et al.(2013)已將它發表於 Wave Motion的期刊。本計畫將嘗試把現有二維模式擴展至三維，並配合成大水工試驗所的實驗來驗證模式之正確性。 This is a two-year research project. A three-dimensional mesh-free numerical model for the simulation of fully nonlinear water waves will be established. The free surface particles in the water wave phenomenon will be traced by using the Lagrangian time marching scheme proposed by Wu and Chang (2011). At each time step the Laplace equation will be solved once then the velocity field can be obtained and the positions of the particles can be predicted for the time marching. For solving the Laplace equation we use the numerical method proposed by Wu and Tsay (2013). This method is a localized mesh-free numerical method so the matrix for solving the unknowns is very sparse. Therefore it is applicable to large-scale practical problems. The combination of the algorithm of Wu and Chang (2011) and the numerical method of Wu and Tsay (2013) has been applied to two-dimensional wave generation problems (Wu et al., 2013). In this study, the two-dimensional wave model in the paper of Wu et al. (2013) will be extended to three-dimensional and will be verified by the comparison with experimental data. Experiments will be carried out in Tainan Hydraulics Laboratory, National Cheng Kung University.

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Development and Application of the Three-Dimensional Mesh-Free Numerical Model for Nonlinear Water Waves

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