淺水波方程式應用於彎曲河道之數值模擬

Numerical Simulation of Shallow Water Equations on the Bend Channel

孫銘寬(Ming-Kuan Sun)

指導教授 ： 鄧志浩

中原大學/工學院/土木工程學系/碩士(2006年)

https://doi.org/10.6840/cycu200600544

摘要

摘 要
以數值模擬方法研究不同河道流場之水面變化。此方法使用最小平方有限元素法 (LSFEM) 求解淺水波方程式 (SWE)。潰壩數值模擬首先模擬一維潰壩與水深、速度、單位流量與福祿數等理論值比較。模擬L 型河道潰壩與45°彎曲型河道潰壩分別與前人研究 Gottardi and venutelli (2004) 和 Lai et al. (2005) 等實驗數據相比較，結果水深變化也都極為接近。最後再將 L 型河道潰壩與 45° 彎曲型河道潰壩初始條件皆假設相同，模擬 S 彎曲型河道相互比較水位雍高，希望能更接近現實情況之河道。
本文研究，發現最小平方有限元素法所得的結果與理論值及其他研究方法吻合，可以有效地呈現出不同河道的水面變化情形。希望結果能為水利工程學界設計應用提供參考。

關鍵字

潰壩 ； 福祿數 ； 最小平方有限元素法 ； 淺水波方程式

並列摘要

Abstract
In this thesis, the flow fields downstream of a broken dam in different kinds of channels were studied by the numerical method. This method applies the least-squares finite element method (LSFEM) to solve the shallow water equations (SWE). For model verification, one dimensional results of dam-break simulation regarding the depth of water, wave speed, discharge per unit width and Froude number are compared with the theoretical solutions.For two-dimensional dam-break simulations, the L-shaped channel and 45° bend channel are compared with the experimental data of Gottardi and venutelli (2004) and Lai et al. (2005), separately .The results show that the depth of water level changes and flow fields are in extremely good agreement with the measurements. Finally, for understanding more about the real channel case, the flow fields in S bend channel is simulated by keeping the same initial conditions as the L-shaped channel. The water heights are compared for this three kinds of channels.
The simulation results of LSFEM are shown to agree with analytical solutions, experimental results and numerical results of other methods. It can effectively appear the water level changes and flow fields in different kinds of channels. It is hoped that the results can be used for the design for the hydraulic engineering.

並列關鍵字

Dam Break ； Least-Squares Finite Element Method ； Froude Number ； Shallow Water Equation

參考文獻

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