水力緩衝區之研究及其應用

The study of hydraulic buffer zone and its applications

洪政暘(Cheng-Yang Hung)

指導教授 ： 黃良雄

國立臺灣大學/工學院/土木工程學研究所/碩士(2009年)

https://doi.org/10.6342/NTU.2009.00178

摘要

本研究利用分區拆解計算方法，並應用緩衝區(Buffer zone)的概念作為分區銜接的方式，以解決在地形劇烈變化處產生的計算不穩定或分區尺度差異太大的問題。緩衝區的概念是將地形劇烈變化處視為灰色地帶且不予計算，或者將緩衝區應用於不同大小尺度區域以達到分區同時計算之效果。此銜接方法雖無法得到相當準確的數值解，但對於地形變化過度劇烈、空間尺度差異過大而導致數值模擬無法計算的問題時，為相當值得採用的方法。

為探討緩衝區銜接方式的可行性，故將緩衝區概念應用於擬三維地下水模式和水平二維水理模式中，並設計單連通區域和複連通區域的案例進行測試。利用克利金法(Kriging)作為內外插工具，並藉由反覆疊代的過程直到緩衝區兩側邊界值滿足收斂條件為止。其中緩衝區在波潮流模式需滿足質量守恆而地下水模式則需滿足能量守恆的方式來銜接。

利用實測資料與緩衝區概念進行模擬，達到不同尺度的網格同時計算的目的，例如河海相接、濁水溪平原設置集水廊道和基樁等案例。

經過無數的測試與案例模擬，結果顯示緩衝區銜接分區的計算能得到相當不錯的成果，顯現緩衝區概念的可行性。緩衝區不規則性的切割法展現其威力與彈性。

關鍵字

單連通區域 ； 複連通區域 ； 水平二維水理模式 ； 擬三維地下水模式 ； 克利金法

並列摘要

In the numerical modeling of flows in oceans, estuaries, rivers or groundwater, the effect of abrupt changes in terrain usually causes numerical instability. In this work,
a numerical treatment using “hydraulic buffer zone” for solving such computational difficulty is proposed. Hydraulic buffer zone is set to be located at the area with
abrupt changes in terrain, and decomposes the computational domain into two subregions. Direct simulation of the flow in the hydraulic buffer zone is ignored, and the connection of the regions divided by the buffer zone is performed using the condition of mass or energy conservation. Hydraulic buffer zone also can be applied to the connection of two computational regions with different spatial resolutions.

In this research, the connecting schemes using hydraulic buffer zone in the modeling of groundwater flow and estuary hydrodynamics are developed. The kriging method is employed to interpolate/extrapolate the water head and water surface elevation across the buffer zone in the groundwater flow modeling and the estuary hydrodynamics modeling, respectively. At every time step, the iterative computations across the buffer zone are performed until the results of two successive iterations converge.

To test the capability of hydraulic buffer zone, several calculations for simplified problems in groundwater and estuary hydrodynamics modeling are performed and reveal reasonable results, including irregular boundary shapes.

Applications to the groundwater modeling in Zhuoshui river and the hydrodynamics modeling in the estuary of the Mei-Luan Creek are given. The results show that the treatment of hydraulic buffer zone is capability of handling the numerical instability caused by the abrupt changes in terrain and connecting two computational regions with different resolutions.

並列關鍵字

Buffer zone

參考文獻

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17.張正緯，”水平分區、垂直分層之三維地下水計算”，國立台灣大學土木工程研究所碩士論文，2007.

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