一維顯式有限解析法模式於交匯渠流之研究

Abstract

本研究係延續Hsu and Yeh(1996)對一維單一矩形渠道數模之成果，發展出適於交匯渠流之數值模式。數值方法則以顯式有限解析法(explicit finite analytic method，簡稱EFA)為架構。EFA的求解精神，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；在匯流處之內部邊界，本文則利用水位相等觀念加以處理。 本文首先以湧浪及潰壩洪水波為例，說明模式於單一渠道中的模擬能力，接著以各種不同角度定量流匯流之實驗資料對本模式進行測試與驗證，最後探討湧浪於主支渠流間的相互影響及上游洪水歷線在主支渠流中的傳遞過程，作為未來實際河道模擬之參考。 模擬結果顯示，對於單一渠道內湧浪與潰壩波之傳遞過程可準確模擬；根據不同角度定量流匯流之模擬結果顯示，以交匯角度分別為22.5及30度時為最佳；湧浪於理想無摩擦損失主支流渠道中傳遞，由於存在初始水深及水面波間之互相來回碰撞，造成流量及流速歷線隨時間起伏之現象。

This study extends Hsu and Yeh’s (1996) one-dimensional open channel flow model for single channels to channels with junction. The numerical model is on the basis of the explicit finite analytic method (EFA). 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 the junction , we use the concept of equal stage. The study first demonstrates the capability of the proposed model for the cases of surge and dam-break wave propogating in a rectangular channel. Second , the junction flow experimental data for various junction angles is adopted to test and verify the model. Finally , the interaction and propogation process of the surge and flood wave through the main channel , the tributary , and the junction are investigated , and these results provide information for river junction simulations in future. According the simulation result , the proposed model can accurately simulate the propogation of the surge and the dam-breake wave in a single channel. For the cases of study junction flows , the cases with junction angles of 22.5o and 30o have the best accuracies compared with the experimental data. For the case of surge propogating in the channel (without friction loss) channel junction , the oscillations of the discharge and velocity hydrographs occur due to the existence of the initial depth of flow and the interaction to and fro of the surge waves between the main and the tributary channels.