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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题名:	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
作者:	劉祐瑄;Yiu-Hsuan Liu
贡献者:	應用地質研究所
关键词:	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;first-type boundary condition;Finite Hankel Transform;third-type inlet boundary condition;advection-dispersion equation;longitudinal and transverse dispersivities;Laplace transform
日期:	2010-08-04
上传时间:	2010-12-09 10:52:20 (UTC+8)
出版者:	國立中央大學
摘要:	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。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.
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