水平分區,垂直分層之三維地下水移流及延散計算法

Computational method for three dimensional adcvection and dispersion in groundwater with horizontal zones and vertical layers

郭遠錦(Yuan-Ching Kuo)

指導教授 ： 黃良雄

共同指導教授 ： 蔡東霖(Tung-Lin Tsai)

國立臺灣大學/工學院/土木工程學研究所/碩士(2004年)

https://doi.org/10.6342/NTU.2004.01647

摘要

為了能夠準確且有效率地描述可溶性地下水污染物在分層非均質土層中濃度之三維分布，吾人除需考慮計算效率外，亦需考慮污染物分布之三維特性。現有諸多模式均以數值方法建構，二維模式計算效率固然高，但無法顧及三維特性，且土層具垂向尺度遠小於水平向尺度之特性。三維模式在數值計算上會造成計算量與計算精確度無法兼顧之困難。因此，原有計算方法需有所更張。本研究之目的為建立一兼具計算效率與精確性之三維地下水移流及延散模式。

本研究將污染物濃度拆解為水平變量(垂向積分平均)與垂向變量之和，再利用垂向積分技巧配合萊布尼茲法則以及擬三維水流之概念，將三維移流延散模式拆解為二維水平變量式(垂向積分平均)以及一維垂向變量式。二維水平變量式採用能夠同時準確計算擴散以及延散等物理現象，且具有無條件收斂以及自動上風法特性的有限解析法(Finite Analytic Method)求取數值解。垂向一維變量式採用解析法求解。本模式經二維式與一維式迭代計算後可模擬三維移流及延散現象，本研究並加入水平分區、垂直分層之計算技巧以模擬非均質土層之傳輸現象。

本模式經解析解比對驗證，結果顯示本研究可模擬非均質土層之移流及延散現象。本模式亦已應用於現地示蹤劑試驗，以顯示本模式之實用性。

關鍵字

移流延散模式 ； 解析解 ； 污染傳輸 ； 有限解析法

並列摘要

In this study an accurate and efficient three dimensional hybrid model has been developed. We need to consider both computational efficiency and the three dimensional characteristic for simulating the convective and dispersive transport in heterogeneous groundwater systems, while the present models are constructed with numerical scheme. Two dimensional models can’t present the three dimensional characteristic while the three dimensional ones are facing the computational difficulties caused by the difference between the length scale of horizontal direction and that of vertical direction. Thus, a new computational method is constructed.

In this study, the three dimensional advective-dispersive equation is decomposed into two-dimensional one (average of vertical integration) and one-dimensional one (vertical variation) by applying the assumption of quasi-three dimensional flow concept and the application of vertical integration technique. The two dimensional horizontal advection- dispersion equation is computed by the finite analytic method which is unconditional stable and is capable of accurately computing the advective-dispersive phenomena. On the other hand, the one-dimensional vertical part is solved analytically. We also add horizontal zones and vertical layers technique for modeling the advective-dispersive phenomena in heterogeneous layered groundwater systems.

The computational results are verified with analytical solutions and in situ field experiments. The results show that the proposed model can indeed simulate the contaminant transport in the groundwater accurately and efficiently.

並列關鍵字

exact solution ； finite analytic method ； mass transport ； advection-dispersion

參考文獻

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