顯式有限解析法模式於超亞臨界混合流之研究

Abstract

本研究延續Hsu and Yeh(1996)之一維顯式有限解析法(explicit finite analytic method，簡稱EFA)模式，發展出適於超臨界流與超亞臨界混合流流況之數值模式。EFA求解之特點，乃在於求解水流動量方程式時，以特性法觀念解得其中變量(流量與通水斷面積)之局部解析解，並且遵守可蘭穩定性條件；邊界處理方面則透過水流之連續方程式與動量方程式，利用特性法觀念求解邊界處之變量；而在超亞臨界混合流況之內部邊界，根據福祿數的大小來判斷水躍發生的位置，且利用內部相鄰計算點的水位高程，透過外插的方式來得到超臨界流區域的下游邊界水深。 為驗證本模式之正確性，本文針對單一坡降矩形渠道、不同坡降矩形渠道問題進行模擬以及分析，且透過與美國陸軍工兵團所研發之HEC-RAS模式的比較，說明本模式模擬之成果與適用性，最後並應用於清水溪草嶺潭堰塞湖上游河段，以探討天然陡坡河道之複雜流況。

This study extends Hsu and Yeh’s (1996) one-dimensional explicit finite analytic model (EFA) for simulating supercritical and mixed supercritical and subcritical flows. The essence of the EFA is the adoption of the concept of method of characteristics to the momentum equation for solving the local analytic solution of the dependent variables (i.e., discharge and cross-section area of flow). To ensure stability of the scheme, Courant condition should be obeyed. The dependent variables at the upstream and downstream boundaries are obtained through the method of characteristics. For the interior boundary condition at mixed supercritical and subcritical flows, the locations of the occurrences of hydraulic jumps are determined according to the values of Froude Numbers. And water depths for supercritical regime at downstream boundaries were calculated. This was done through the method of external interpolation, by utilizing the water surface elevations of the interior neighboring computational points. To test the accuracy of the model, this study simulates and analyses the cases on both a single and different slopes of rectangular channels. To elaborate the functionality and suitability of this model, these simulated results were then compared with the ones done by the HEC-RAS model, developed by the US Army Corps Engineers. Finally, the study applies the results from the model to the upstream of Chin-Shui River at Tsaoling landslide dam area, and discusses the flow condition of natural river.