二維有限域溶質傳輸解析解模式發展

Analytical solutions for two-dimensional advective-dispersive equation in a finite spatial domain

凃佑霖(You-lin Tu)

指導教授 ： 陳瑞昇

國立中央大學/地球科學學院/應用地質研究所/碩士(2015年)

摘要

地下水污染傳輸模式是了解預測地質介質中污染物傳輸的重要工具，然而前人研究常假設出流邊界長度為無窮遠，此假設不符合實際情況，而有限邊界多為一維系統，無法適當描述現實問題。本研究目的為發展有限域二維溶質傳輸解析解模式，考慮移流、延散傳輸、線性平衡吸附、一階衰減項和源/匯項，以描述二維溶質的傳輸行為，進一步考慮初始、邊界條件和源/匯項為Dirac delta、常數、Heaviside step、週期性正弦或指數衰減函數。解析解推導主要是連續使用各種積分轉換消去時間微分項與空間微分項，將偏微分方程式轉換為代數方程式，再由一系列逆轉換求得完全顯示解析解。本研究發展之解析解與有限差分(Finite difference method)數值方法進行相互驗證，兩者的驗證結果十分吻合。此模式可應用於週期性正弦函數的參數推估，以推求現地在有限資料中的延散係數，且可適當使用於現地尺度場址中，了解污染物傳輸行為且作為初步污染整治的基礎，此模式可作為數值模式測試與驗證的工具。

關鍵字

污染傳輸 ； 移流-延散方程式 ； 二維 ； 有限域 ； 解析解

並列摘要

Contaminant transport model is an important tool for predicting and describing the movement of contaminants in the subsurface. However, most of analytical solutions are developed only for infinite or semi-infinite spatial domains. One primary use of analytical solutions is to test numerical models that compute solutions on finite domains, it would be very useful to also have analytical solutions for finite domains. The object of develop an analytical model for two-dimensional advection-dispersion equation in a finite domain. The model involves a wide variety of time-dependent boundary inputs, spatial-dependent initial distributions, and time- and spatial-dependent zero-order productions. The analytical solutions are obtained by successively applying different integral transforms corresponding to the governing equations and its associated initial and boundary conditions. The analytical solutions are verified against the numerical solutions using a finite difference scheme. Results show perfect agreements between the analytical and numerical solutions. This model can be applied to estimate the source of the periodically sinusoidal functions in the few information field data, to simulate the transport of temporal change in contaminant source releases. The model useful for testing or benchmarking numerical transport codes because of the incorporation of a finite spatial domain.

並列關鍵字

Contaminant transport ； advection-dispersion equation ； two-dimensional ； finite domain ； Analytical solution

參考文獻

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