第三類注入邊界條件二維圓柱座標移流-延散方程式解析解發展

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劉祐瑄(Yiu-Hsuan Liu) 查詢紙本館藏

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應用地質研究所

論文名稱

第三類注入邊界條件二維圓柱座標移流-延散方程式解析解發展
(Analytical model to two-dimensional advection–dispersion equation in cylindrical coordinates subject to third-type inlet boundary condition)

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摘要(中)

本研究發展第三類注入邊界條件下二維圓柱座標移流-延散方程解析解建立以描述地表下圓柱座標系統之二維溶質傳輸情形。為建立第三類注入邊界條件二維圓柱座標移流-延散方程解析模式，採用finite Hankel轉換技巧結合Laplace轉換以求得解析解。將建立的第三類注入邊界條件解析模式與前人文獻所得到的第一類注入邊界條件解析模式做比較，以說明兩者對於溶質傳輸情形之影響。結果顯示當觀測點靠近注入邊界與地下水傳輸系統之縱向延散係數大時，兩解析解因注入端邊界之延散項差異而導致濃度穿透曲線不符合。所發展的解析模式可應用於同時決定縱向與側向延散度的二維圓柱實驗室土柱試驗或入滲追蹤劑試驗。

摘要(英)

An exact analytical solution for two-dimensional advection-dispersion equation (ADE) in cylindrical coordinates subjected to the third-type inlet boundary condition is developed to describe the two-dimensional solute transport in a subsurface system with cylindrical geometry. The finite Hankel transform technique in combination with the Laplace transform is adopted to solve the two-dimensional ADE in cylindrical coordinates. The developed exact analytical solution is compared with the solution with first-type boundary condition available in literature to illustrate the influence of inlet boundary condition on solute transport. Results show that the significant discrepancies between breakthrough curves obtained from two analytical solutions, especially for observation point near the inlet boundary or a subsurface system large longitudinal dispersion coefficient. The developed solution is an efficient tool for simultaneous determination of the longitudinal and transverse dispersivities from a two-dimensional laboratory-scale radial column experiment or a infiltration test with a tracer.

關鍵字(中)

★ 縱向與側向延散度
★ 移流-延散方程式
★ 第三類注入邊界條件
★ finite Hankel轉換
★ Laplace 轉換
★ 第一類注入邊界條件

關鍵字(英)

★ first-type boundary condition
★ Finite Hankel Transform
★ third-type inlet boundary condition
★ advection-dispersion equation
★ longitudinal and transverse dispersivities
★ Laplace transform

論文目次

目錄
摘要 i
Abstract ii
目錄 iii
圖目錄 v
表目錄 viii
符號說明 ix
一、前言 1
1-1 研究動機 1
1-2 文獻回顧 5
1-3 研究目的 8
1-4 論文架構 9
二、第三類注入邊界條件二維圓柱座標系統移流-延散解析數學模式 11
2-1 基本假設與模式建立流程 11
2-2控制方程式與邊界條件 13
2-3 解析解推導 23
三、結果與討論 35
3-1模式驗証 35
3-1-1解析模式數值收斂誤差 35
3-1-2解析模式驗証 42
3-2 模式模擬與參數敏感度分析 45
3-3 第一類注入邊界與第三類注入邊界解析模式比較 50
四、結論與建議 55
參考文獻 56
附錄一 Laplace-finite Hankel域求解 59
附錄二 Laplace轉換有限差分模式建立 61
附錄三第一類邊界圓柱座標移流-延散解析模式 64
附錄四現地三環入滲追蹤劑試驗 66

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指導教授

陳瑞昇(Jui-Sheng Chen)

審核日期

2010-8-4

推文