有限解析法模式於渠道變量流之模擬

Abstract

本研究係以顯式有限解析法為架，構針對一維渠道之緩變及急變水流進行模擬分析。潰壩洪水波為水力學上重要研究對象之一，從在矩形渠道之解析解，至非稜柱水槽之水工模型實驗，以及其他數值模式的發展，皆以準確描述洪水波於渠道中傳遞為目標。本研究發展之有限解析法模式，以Chow之乾床潰壩波解析解、Bellos等之二維潰壩試驗資料及Savic等之修正 Godunov法模擬結果來驗證本模式，在遵守顯式法之穩定條件下，採最大允許時間間距所模擬之結果頗佳。最後，以阿公店溪下游河道為實際河川模擬的對象，考慮沿途支流所匯入之側流量，模擬五十年頻率之洪水；另在不考慮側流量下發生潰壩時，探討潰壩波在河道中傳遞的過程。

This study aims at the simulation of gradually and rapidly 1-D openchannel flow based on the explicit finite analytic method. The investigation on dam-break wave is one of the important topics in Hydraulics. The analytic solutions in the rectangular channels, hydraulic experiments in irregular channels, and development of numerical models have the purpose of trying to accurately describe propagation of dambreak waves in open channels. in this study, the proposed explicit finite analytic model is first validated by comparing the simulated results with the analytic solution derived by Chow for dry-bed dam-break wave, Bellos et al.'s 2-D dam-break experimental data, and Savic's results based on the modified Godunov method. By obeying the stability condition for the explicit scheme, simulated results based on the adoption of allowabie maximum time the increments are quite good. Finally, the downstream reach of Ah-Gong-Diann River is used as the real case for simulation. The propagation of the 50-yr flood as well as the lateral inflows is simulated. In addition, propagation of the dam-break wave along the River, without lateral inflows, is also studied.