顯式法於明渠穿臨界流上的應用

本文以MacCormack顯式法來解de St. Venant方程組，並由特性線法解邊界條件。首先以傳統的潰壩等解析解驗證此模式，然後再模擬出定常水躍、非定常水躍、尾端下射式閘門之控流過程與流經凸起物之變動局部超臨界流況等計算例，目的在探討MacCormack法於穿臨界流上的應用可行性。結果發現MacCormack法於定常水躍與非定常水躍的模擬中能自動找出變動水躍的位置及高度，而於下射式閘門中能成功模擬出負湧浪的情況，並應用於流經凸起物之陡變地形，使凸起物下游處產生局部水躍。模擬結果合理，只有些許數值震盪誤差，需要人工平滑處理。可適用於本省河川上游區段陡坡超臨界流與深潭交互產生的山區河溪情況。

關鍵字

MacCormack法； de St. Venant方程組；穿臨界流；水躍

並列摘要

MacCormack scheme as an explicit numerical scheme is assessed in solving de St. Venant equations for one-dimensional unsteady open-channel flow. Method of characteristics is employed to obtain the next-time values at upstream and downstream boundary points. Classical dam-break problem, positive/negative surges with analytical solutions, and mass conservation of flow are used to verify this model. Cases of unsteady flows with different controls are discussed in this article, which include stationary hydraulic jump, unsteady jump, unsteady flow induced by a sluice gate, and unsteady flow past a deposition mound. The applicability of this scheme in transcritical flow condition is accessed. Results indicate that tracking of the hydraulic discontinuity in the case of sudden change from supercritical to subcritical flow is automatic, which makes this scheme suitable for simulating mountain river in Taiwan. In the case of unsteady flow past a deposition mound, a negative surge is created by opening a sluice gate, and a local supercritical flow is successfully simulated. Artificial viscosity is necessary in smoothing numerical oscillation inherited from this explicit, second order scheme.

並列關鍵字

MacCormack scheme ； de St. Venant equations ； Transcritical flow ； Hydraulic jump

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