水力傳導係數差異巨大的分區地下水流
分析與計算

地下水分布區域極大，全三維計算之垂向深度與水平距離尺度比例差異懸殊造成計算量龐大但精度偏低等問題產生。因此本文引入以ε為小、大水力傳導係數之比為擾動參數之正規擾動法(Regular Perturbation Method)展開將零階、ε階、ε2階 ……各階分階展開處理在水力傳導係數相差巨大之區域使地下水模式更趨完備與多樣性。本研究將改善蔡東霖(2001) 開發之地下水流模式，蔡(2001)對於地下水流模式之計算，提出分層之概念，將土體作垂直分層或虛擬分層，在假設土層速度勢(即壓力)於垂向深度上為二次多項式函數分布下，引用分層垂向積分技巧，層與層間之交界面邊界以速度勢(即壓力)及通量連續之條件加以連接。其中在計算水平方向水力傳導係數相差巨大之地區略顯不足，故本研究將對此模式加以研究讓模式有更佳的方法。本研究以微小之ε值為基礎進行正規擾動法(Regular Perturbation Method)展開，經過擾動法將邊界區分為零階和ε階，接著利用拉普拉斯方程(Laplace Equation)求解零階和ε階得其解析解。其次，利用有限差分法(Finite Difference Method)同樣的求解零階和ε階並與解析解作比對驗證模擬結果是否吻合以顯示本模式之合理性。

關鍵字

正規擾動法；有限差分法；水力傳導係數相差巨大之區域

並列摘要

Groundwater has a wide range distribution in all kinds of terrain. A huge order difference between the horizontal and vertical depth scale may cause the problem of massive computation and low accuracy in complete three dimensional groundwater flow. In dealing with this kind of problem, by using regular perturbation theory to separate the exact solution to the first order term and the higher-order terms, which could deal with large hydrodynamic conductivity difference in the groundwater computation and make the computation model of groundwater much more complete and diversified. In this study, the groundwater flow model follows Tsai’s(2000), the concept of layered three-dimensional groundwater flow simulation is proposed. Every layer is vertically integrated with an assumption that satisfies quadratic polynomial function and the interface between two layers must satisfies the continuity of pressure and flux too, however, the model is not efficient on dealing with large hydrodynamic conductivity difference in the groundwater computation, we continue and improve the development of this model to make the model better. The present study is introduced in the regular perturbation expansion of solving the boundary value problem for order(0) and order(ε) by Laplace Equation. Second, compute the same case by using Finite Difference Method to test how reasonable and match of the exact solution and the numerical methods.

並列關鍵字

Perturbation Theory ； Finite Difference Method ； The Area of Large Hydrodynamic Conductivity Difference

參考文獻

12.王元亨. (2013) “山區地下水與質量傳輸模式”. 國立台灣大學碩士論文.

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4.S.P. Neuman , C. Preller and T.N. Narasimhan (1985). “Adaptive Explicit-Inplicit Quasi Three-Dimensional Groundwater Solute Transport”.

6.Ching-Jen Chen (1995). “Finite Analytic Numerical Method in Flows and Heat Transfer”.

國際替代計量

水力傳導係數差異巨大的分區地下水流分析與計算

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