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研究生： 葉銘凱
Yeh, Ming-Kai
論文名稱： 使用連續時間隨機漫步法於污染傳輸模擬之研究
The study of using continuous time random walk model in contaminant transport modeling
指導教授： 徐國錦
Hsu, Kuo-Chin
學位類別： 碩士
Master
系所名稱： 工學院 - 資源工程學系
Department of Resources Engineering
論文出版年： 2007
畢業學年度： 95
語文別： 中文
論文頁數： 98
中文關鍵詞： 連續時間隨機漫步 、非高斯分佈 、平流擴散方程
外文關鍵詞： non-Gaussian, continuous time random walk
相關次數： 點閱：132  下載：1 
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    • 由於現地的土壤種類之空間分佈是不均勻的，而其物理化學特性直接影響到污染物之傳輸行為，因此污染現象經常呈現非高斯之分佈，使用傳統隨機漫步理論並無法適當地模擬現地污染傳輸之行為。本研究使用連續時間隨機漫步模式探討土壤特性影響污染物質之傳輸過程，藉以模擬非高斯分佈的污染傳輸行為。研究中定出連續時間隨機漫步模式所需之參數與傳統平流擴散方程之關係，並且以 Borden場址為例，驗證連續時間隨機漫步模式之可用性，結果顯示連續時間隨機漫步模式配合序率理論之延散係數值可適當地描述溶質傳輸之行為。

    Due to the heterogeneities of physical and chemical properties of porous media, the plumes of contamination are often shown non-Gaussian behaviors. We proposed a numerical model to simulate non-Gaussian distribution by using the continuous time random walk(CTRW) method. The parameters required in the CTRW model are defined by fitting results of CTRW and these of traditional advection-dispersion model. The proposed model is applied to Borden site. Results show that CTRW well describes the non-Gaussian behavior of solute transport and is a better model to simulate the contaminate transport.

    摘要………………………………………………………………I Abstract…………………………………………………………II 誌謝………………………………………………………………III 目錄………………………………………………………………IV 表目錄……………………………………………………………VII 圖目錄……………………………………………………………VIII 符號說明…………………………………………………………XII 第一章 緒論……………………………………………………1 1.1 研究動機與目的……………………………………………1 1.2 前人研究……………………………………………………2 1.3 研究大綱……………………………………………………5 1.4 研究方法與流程……………………………………………6 第二章 污染傳輸理論與模擬…………………………………7 2.1 溶質傳輸……………………………………………………7 2.1.1 平流 ( Advection )……………………………………7 2.1.2 擴散及延散 ( Diffusion and dispersion ) ………8 2.2 延散通量……………………………………………………11 2.3 求解延散係數的方法………………………………………13 2.4 流體運動方法之描述………………………………………14 2.5 尤拉法………………………………………………………15 2.5.1 平流延散方程之推導 ( Eulerian Method )…………15 2.5.2 尤拉數值方法……………………………………………18 2.5.3 一維溶質傳輸模式………………………………………19 2.6 拉氏隨機漫步模式(Lagrangian random-walk model)…23 2.7 選用拉氏隨機漫步模式之原因與探討……………………24 2.8 布朗運動的特性與發展……………………………………28 2.9 擴散係數與平方位移關係…………………………………30 2.10隨機變數……………………………………………………31 2.11連續時間隨機漫步…………………………………………32 2.12宏觀延散係數………………………………………………33 第三章 隨機漫步模式…………………………………………34 3.1 單純隨機漫步………………………………………………34 3.2 連續時間隨機漫步…………………………………………37 3.2.1 CTRW-1……………………………………………………38 3.2.2 CTRW-2……………………………………………………41 3.2.3 Levy motion ……………………………………………43 3.2.4 Levy flight ……………………………………………44 3.3 不同粒子數量時模擬結果之影響…………………………45 3.6 粒子質量的運算……………………………………………47 第四章 連續時間隨機漫步模式之建立與現地應用…………48 4.1 均勻分佈之隨機為移步伐…………………………………48 4.2 常態分佈之隨機為移步伐…………………………………53 4.3 均勻與常態分佈位移步伐隨機漫步模擬結果之比較……55 4.4 停滯機率與遲滯係數的關係………………………………56 4.4.1遲滯速度與平流停滯機率的關係式 ……………………60 4.4.2遲滯速度與延散停滯機率的關係式 ……………………62 4.5 宏觀延散係數………………………………………………64 4.6 場址的模擬與介紹…………………………………………67 4.6.1 場址資料 ……………………………………………67 4.5.2 場址的模擬………………………………………………69 4.7結果與討論 …………………………………………………76 第五章 結論與建議……………………………………………77 參考文獻…………………………………………………………80 附錄………………………………………………………………86 附錄1 CTRW1 ……………………………………………………86 附錄2指數相關函數之縱向延散傳輸 …………………………89 附錄3 Levy motion ……………………………………………92 自述………………………………………………………………98

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