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.

中文摘要 i
英文摘要 ii
致謝 iii
目錄 iv
表目錄 vii
圖目錄 viii
符號說明 ...xi
第一章 緒論 1
1.1 前言 1
1.2 研究方法 2
1.3文獻回顧 2
1.4 論文架構 10
第二章 理論基礎 12
2.1基本假設 12
2.2控制方程式 13
2.3 顯式有限解析法簡介 13
第三章 數值方法 16
3.1模式建立架構 16
3.1.1控制方程式之離散化 16
3.1.2外部邊界條件 18
3.1.3內部邊界條件 19
3.1.4斷面處理方式 24
3.2穩定性分析 25
3.3交錯格網 27
3.4模式演算之流程 28
第四章 模式驗證 30
4.1主支流交匯之分析 30
4.1.1等寬匯流交匯角度為45度 30
4.1.2等寬匯流交匯角度為90度 32
4.1.3非等寬匯流交匯角度30度、60度 33
4.2 主、分流之分析 34
4.2.1 等寬分流角度為90度 34
4.2.2 等寬分流角度為75度 36
4.3 模擬成果評估 38
4.3.1 一維EFA模式與實驗之比較 38
4.3.2 合、分流模擬 37
第五章 案例模擬 40
5.1 合流模擬 40
5.2 分流模擬 42
第六章 結論與建議 45
6.1結論 45
6.2建議 47
參考文獻 48
附錄一 顯式有限解析法係數推導 90
附錄二 特性線之推導 94

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