Numerical Study of Wave Propagating over a Submerged Bar on Sloping Bottom

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Project title

Code/計畫編號

NSC100-2221-E019-004-MY3

Translated Name/計畫中文名

方向不規則波通過斜坡地形上潛堤變形之研究-子計畫二：斜坡地形效應對波浪通過潛堤變形之數值研究

Project Coordinator/計畫主持人

Shin-Jye Liang

Funding Organization/主管機關

National Science and Technology Council

Department/Unit

Department of Marine Environmental Informatics

Website

https://www.grb.gov.tw/search/planDetail?id=2350407

Year

2011

Start date/計畫起

01-08-2011

Expected Completion/計畫迄

01-07-2012

Bugetid/研究經費

433千元

ResearchField/研究領域

土木水利工程
海洋科學

"利用數值方法模擬波浪與地形間之交互作用是一項極富挑戰之問題，主要的困難在於波浪與地形間之藕合、非線性、以及所造成之複雜波浪變形等。本研究中，我們將使用空間時間最小平方有限元素法，求解淺水方程式 (Shallow-Water Equations, SWE) 與布氏方程式 (Boussinesq equations, BE)，並模擬方向規則波和不規則波通過等向斜坡潛堤之波浪變形。在先前的研究中，我們利用最小平方有限元素法求解 Stokes 與 Navier-Stokes 方程式 (8/2004 ~ 7/2005, NSC 94-2218-E-035 -011-)、淺水方程式 (8/2005 ~ 7/2006, NSC 95-2221-E-019-095-)、以及Korteweg-de Vries (KdV) 方程式，並成功地將模式應用於各種水流和波浪之模擬，例如潰壩問題、波浪變形、波浪與地形間之交互作用，以及波浪與結構物之交互作用等。本研究中，我們將利用空間時間最小平方有限元素法（Space-Time Least-Squares Finite-Element Method），求解淺水（SWE）與布氏（BE）方程式，將 SWE 與 BE 模式應用於波浪通過等向斜坡潛堤地形之波浪變形，並與實驗數據（子計畫4）比較，且有系統地比較SWE 與 BE 模式之適用條件、計算準確度與效能。許多與「空間時間最小平方有限元素」數值方法與「波浪與地形間之交互作用」應用之議題，將在本研究中有系統地探討。第一年 (8/1/11 ~ 7/31/12) ： - 模擬正向與斜向規則波通過等向斜坡潛堤之波浪變形 - 探討邊界條件設定 (輻射邊界、入射邊界及吸收邊界) 等數值技巧對計算結果之影響第二年 (8/1/12 ~ 7/31/13) ： - 模擬正向不規則波通過等向斜坡潛堤之波浪變形，模式中將加入碎波與能量消散之影響機制，使計算結果更能適切地描述實際現象 - 比較SWE、BE、MSE & SWAN 模式計算結果第三年 (8/1/13 ~ 7/31/14) ： - 模擬方向不規則波通過等向斜坡潛堤之波浪變形，探討波浪與地形、潛堤之交互作用 - 比較SWE 和 BE 模式計算結果與實驗數據（子計畫4）" "Numerical modeling of interactions of wave-bathymetry is challenging. The main difficulties arise from the coupling of wave and bathymetry, the nonlinearity of the system, and the induced complex wave deformations. In this study, a space-time least-squares finite-element method (space-time LSFEM) for shallow-water equations (SWE) and Boussinesq equations (BE) will be developed and applied to simulate wave deformations of directional regular/irregular waves on a constant sloping bottom. LSFEM has been developed and applied to Stokes and Navier-Stokes Equations (8/2004 ~ 7/2005, NSC 94-2218-E-035 -011-), shallow-water equations (8/2005 ~ 7/2006, NSC 95-2221-E-019-095-), and Korteweg-de Vries (KdV) equation in our previous study. The models have been successfully applied to various flow and wave simulations, including dam-breaking, wave deformations, wave-bathymetry interactions, and wave-structure interactions. In this study, the space-time LSFEM SWE and BE models will be developed. Both models will be used to simulate wave deformation and wave-bathymetry interactions. Computed results will be systematically compared with experiment data (sub-project 4). Several issues relevant to space-time LSFEM, and application of the SWE and BE model to wave-bathymetry interactions are to be investigated: 1st year (8/1/11 ~ 7/31/12): - use a normal and oblique regular wave passing over a submerged bar on a sloping bottom as a test example, and systematically compare computed results of SWE and BE model - compare the treatment of boundary conditions (radiation boundary condition and reflective boundary condition) in weak sense through the least-squares functional as suggested by Pontaza and Reddy (2003) with the strong sense that used by most other numerical methods. 2nd year (8/1/12 ~ 7/31/13): - to simulate directional irregular waves passing over a submerged bar on a sloping bottom - to systematically compare computed results of , BE, SWE & SWAN model 3rd year (8/1/13 ~ 7/31/14): - to simulate a regular/ irregular wave passing over a submerged bar on a sloping bottom, and systematically compare computed results of MSE, BE, SWE & SWAN model with experiment data (sub-project 4)"

Keyword(s)

淺水波方程式
布氏方程式
潛堤
最小平方有限元素法
Shallow Water Equations
Boussinesq Equations
Submerged Bar
Least-Square Finite Element Method

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Numerical Study of Wave Propagating over a Submerged Bar on Sloping Bottom

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