一維有限解析法模式於明渠合分流之研究

Abstract

本文延續Hsu & Yeh (1996)之一維有限解析法模式應用於單一矩形明渠流之模擬，將之擴充至含主支流渠道之合分流模擬。本模式採交錯格點，並符合可蘭穩定條件下求解。在合、分流交匯區之內部邊界條件係以水位相等來處理；在上下游邊界處，則根據流況需要，給予流量或水位。為驗證本模式之精度，本文利用淡江大學之模型試驗資料來加以比較。針對主支流合流角度為30、45、60及90度，分流角度為75及90度之試驗進行數模，經由合流前上游之主、支渠水深比較與分流後之主渠下游流量比較結果顯示，除90度合流在高流量比情況下，於支渠上游水深有稍高之誤差外，其餘案例均有頗令人滿意之模擬結果。此外，並模擬非定量流合、分流之假設案例，在角度30度下，所得之結果皆在一合理範圍內。

This study is an extension of Hsu & Yeh’s (1996) 1-D explicit finite analytic model for single rectangular channel flow simulation. The extended model has the capability of simulating junction and division flows. The solutions on staggered grids are obtained by obeying the Courant condition. Equal stage is adopted as the internal boundary condition at the junction or division; the discharge or stage is specified at the upstream or downstream boundary according to the given flow characteristics. To test the accuracy of the model, we compare the simulated results with Tamkang University’s experimental data. The numerical simulations include the cases with junction angles of 450 and 900, and division angles of 750 and 900, respectively. For junction flows, the upstream depths in the main channel and the branch channel are compared; for division flow, the downstream depths in the main channel are compared. The simulated results are satisfactory except the cases of junction flow with junction angle of 900 and high discharge ratios. Under this condition, the simulated depths in the upstream branch channel are lower than those obtained from experiments. In addition, the simulation results for unsteady junction and division flows with angles of 300 are satisfactory.