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標題: Study on the numerical model with nonlinear and transient moving boundary
作者: Yan-Chi Chen
Chih-Hua Chang
Ping-Cheng Hsieh
關鍵字: Moving boundary;Fully nonlinear wave;Free surface;transient boundary-fitted coordinate system;移動邊界;完全非線性;自由液面;貼壁坐標
Project: 水土保持學報, Volume 45, Issue 4, Page(s) 791-802.
台灣地區四面環海,海岸線長約1,139 公里,海岸侵蝕造成的國土流失為一項重要的課題,一但國土被侵蝕就很難再恢復原狀,其可能衝擊沿海的各種產業,如工業、觀光業、養殖業。甚至造成沿海居民受災風險增高與沿海居民向內陸移居。而造成海岸侵蝕的原因主要為風力與海浪這兩者,而本文主要為討論海浪之部分,藉由研究海浪之特性以防止海岸之侵蝕。本研究應用曲線坐標順應瞬時變動之自由表面邊界,以勢能流函數發展二維完全非線性水波模式,探討其以淺水波理論給予初始條件的適宜性。模式採用貼壁坐標配合有限差分法求解完全非線性自由液面條件及拉普拉斯勢能流流場方程式。計算問題注重在初始條件的探討。在模式印證部份,分析孤立波在平底床渠道長距離傳遞的計算結果。以孤立波的特性可維持非線性與頻散性平衡而維持波形不變的情況下以定速移動。結果發現淺水波的初始條件置入本模式完全非線性條件,波高會輕微降低,尾波會產生少許的不規則波,但在計算過程中逐漸調整滿足完全非線性的條件至收斂解。模式將滿足非線性條件移動長時間的孤立波數值解擷取其收斂解重新作為初始條件,則可明顯減小尾跡波的情形。

The coastline of Taiwan, an island all surrounded by the sea, is about 1,139 km long. Land loss caused by coastal erosion is an important issue. Once the erosion of land was difficult to restitution, it may impact the coastal variety of industry, tourism, and aquaculture. Moreover, it will also result in the increasing risk of coastal residents and the affected coastal residents move inland. The coastal erosion was mainly due to wind and waves effects, and this study is aimed at discussing the effects of the waves in order to prevent the erosion of the coast. This study is to develop a two-dimensional fully-nonlinear wave model of potential function. A transient curvilinear coordinate system is applied to fit the moving free surface. The main subject is focused on the initial condition problem. This model is combined with boundary-fitted grid and a fast finite-difference method to discretize the free-surface boundary conditions and the Laplace equation of potential function. It is known the solitary wave can travel with a constant speed and keep its symmetric shape because of its balance of nonlinearity and dispersion. It is convenient to impose our initial condition using Boussinesq analytic solution. However, there will be a series of weak trailing waves occurred behind the main wave, and the main wave amplitude is tiny smaller than that of the incident one. After the wave propagating a long distance, computational converged solution is gradually adjusted to satisfy the fully-nonlinear conditions. The main wave can fling the trailing waves. Thus, we cut the zone of computational solution as the initial condition of incident wave. It is shown this feedback can eliminate the trailing waves of solitary wave.
Appears in Collections:第45卷 第04期

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