迴水影響下圓管流解析法與數值法

Analytical and Numerical Solution of Circular Flow where Backwater Occurs

許冬福(Tung-Fu Hsu)

指導教授 ： 王士紘

淡江大學/工學院/水資源及環境工程學系碩士班/碩士(2010年)

https://doi.org/10.6846/TKU.2010.00882

摘要

目前解決圓型渠道變量流之洪流演算問題時，大部份是使用套裝軟體或由數值方法來評估，其中所使用之數值方法乃是將渠道變量流中動量方程式得慣性項忽略不計，並將方程式予以線性化，結果與非線性動力波模式非常接近。
但在計算過程中，因其省略慣性項之故，運用在圓型渠道或下游有迴水影響情況時常與實際情況有所落差，不太滿足工程實用價值，故本論文便以圓型渠道變量流之初步線性解析解與一維性Saint-Venant動力波模式數值解做比較，另外對於下游邊界條件受迴水影響時，兩者之間是否有更大誤差做一比較。
由結果可得知數值解有部份計算誤差，與解析解誤差較大，又解析解較為接近真解，且其計算應用便利，故解析解具有簡易、經濟、有效率、準確之工程實用價值。

關鍵字

聖凡納方程式 ； 解析解 ； 下游邊界條件 ； 迴水效應 ； 數值方法

並列摘要

At present when solves mighty current of calculation problems which unsteady circular flow, the major method is using the coverall software or the numerical methods which be used by the momentum equation in the unsteady open channel flow in the inertia item to be ignored, and make the equation linearization, and the results is almost the same to complete dynamic wave model .
But therefore in the computational process, because of its abbreviation inertia item, utilizes in the circular channel or the downstream which the backwater occurred. It often makes a little difference with the actual situation, and is not enough to satisfy project of engineering, therefore the present paper use the preliminary linear analytical solution and the one dimension Saint-Venant equation with numerical solution does by the circular flow compares. On the other way, regarding that downstream boundary condition with backwater effect, as soon as whether between both to have bigger errors to do compares.
By the results may know that the numerical solution has the counting error which bigger than the analytic solution, and then analytical solution is closer to genuine solution, and its computation and application is more convenience, therefore analytical solution may be understood that is simple ,economic, effectiveness, the accurate project use value.

並列關鍵字

Saint-Venant Eq. ； Analytical ； Boundary ； Backwater ； Numerical

參考文獻

4. Dooge, J.C.I. Kundzewicz, Z.W. and Napiorkowski, J.J, ” On Backwater Effects in Linear Diffusion Flood Routing”，Hydrological Science，28.3.9.，1983，pp391-402。

7. S.H Wang，” A Study on the Analytical and Numerical Solution for Unsteady Open Channel Flow with Circular Cross Section”，台灣水利季刊第36卷，第二期，1988.06，pp.50-56。

14. P. G. Samuels, and C. P. Skeels，” Stability Limit for Preissmann’s Scheme，” Journal of Hydraulic Engineering，ASCE，Vol. 116，No. 8，August，1990，pp.997~1012。

參考文獻

1. Mahood, K. and Yevjevich, V.,ed.，” Numerical Methods of Solution of the Unsteady Flow Equation”，Chap.4，Vol. 1，pp89-182.，1975。