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

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Project title

Code/計畫編號

MOST104-2221-E415-020

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 (II)

Project Coordinator/計畫主持人

Nan-Jing Wu

Funding Organization/主管機關

National Science and Technology Council

Co-Investigator(s)/共同執行人

蕭士俊

Department/Unit

Department of Civil and Water Resources Engineering,NCYU

Website

https://www.grb.gov.tw/search/planDetail?id=11564842

Year

2015

Start date/計畫起

01-08-2015

Expected Completion/計畫迄

31-07-2016

Bugetid/研究經費

508千元

本計晝為科技部專題研究計晝「非線性水波三維無網格數值模式之發展與應用」之第二期。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.(2014)已將它發表於Wave Motion的期刊。前一期之計晝，已初步將現有二維模式擴展至三維，並能模擬固定邊界數值造波的問題。下一階段，將繼續將模擬擴充，使之能模擬變動邊界之造波現象，比如：三維海底地形崩移及海岸地形崩移海嘯波生成。此外，亦將嘗試分析三維的水槽盪漢、或是物體在海床上移動所產生之水面波等問題。 This is the continuing research of the project entitled “Development and Application of the Three-Dimensional Mesh-free Numerical Model for Nonlinear Water Waves.” 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. In the past year, the two-dimensional wave model in the paper of Wu et al. (2014) has been extended to three-dimensional. Incident wave problems have been simulated and the model has been verified by the comparison with experimental data. In this study, we will do some further extension to make the model capable to simulate waves generated by moving boundaries such as tsunamis caused by landslides, liquid sloshing in a 3-D tank, or surface waves generated by moving submerged objects.

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

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