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姓名 林宛瑩(Wan-Ying Lin) 查詢紙本館藏 畢業系所 數學系 論文名稱
(Mathematical Modeling and Numerical Simulation for Transport Phenomena in Porous Medium)相關論文 檔案 [Endnote RIS 格式]
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摘要(中) 本篇論文目的在於理解地下水運動的規律和地下水環境,探討並建立地下水運動的
數學模型。論文中,我們設定我們的環境為飽和層中溶質的地下水傳輸,我們著重於地
下水中溶質的濃度傳輸在通過多孔介質時所遵循的物理現象。溶質傳輸模式受移流、延
散、擴散影響。並探討地下水溶質運移所涉及的物理參數或經驗參數,以及這些參數的
表達方式和物理意義。地下水溶質在地下水環境的一些化學反應,也會影響濃度的傳輸
分布,如放射性衰變、注入與開採、吸附與解吸,加以考慮這些化學反應,使數學建模
更能貼近現實環境。採用一些數值方法以及數值模擬溶質在地下水環境中,當受到移
流、擴散、反應、孔隙度等的不同狀態影響下,地下水在計算範圍內濃度的傳輸分布情
形。摘要(英) This study discussed the law of groundwater movement and the groundwater environment, and constructed a mathematical model of groundwater movement. The environment
was set as groundwater transport of solute in the saturated layer. The focus of this study
was the physical phenomenon of concentration of solute in groundwater through porous
medium. The solute transport model was influenced by advection, dispersion and dif-
fusion. The physical parameters or empirical parameters related to groundwater solute
transport and the mode of expression and physical significance of these parameters were
discussed. Some chemical reactions of groundwater solute in the groundwater environment
also influenced the migration and distribution of concentration, such as radioactive decay,
infusion and exploitation, adsorption and desorption. These chemical reactions were con-
sidered to approximate the mathematical modeling to real environment. Some numerical
methods and values were used to simulate the solute in groundwater environment, the
concentration migration and distribution of groundwater in the computing range under
the effects of advection, diffusion, reaction and porosity.關鍵字(中) ★ 多孔介質
★ 飽和層
★ 移流
★ 延散
★ 擴散
★ 吸附與解吸關鍵字(英) ★ Porous medium
★ saturated layer
★ advection
★ dispersion
★ diffusion
★ adsorption and desorption論文目次 List of Figures vi
List of Tables ix
1 Introduction 1
2 Ground Water Hydrology 5
2.1 Vertical Distribution of Ground Water System . . . . . . . . . . . . . . . . 5
2.2 Darcy’s Law . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
3 Solute transport in groundwater model 11
3.1 Groundwater solutes transport phenomenon . . . . . . . . . . . . . . . . . . 11
3.2 Derivation of the Advection-Dispersion Equation for Solute Transport . . . 15
3.3 Reaction-Advection-Dispersion Equation . . . . . . . . . . . . . . . . . . . 19
3.4 Dimensionless Equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24
4 Numerical method 26
4.1 The Finite-Difference Method . . . . . . . . . . . . . . . . . . . . . . . . . . 26
4.2 explicit method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27
4.3 implicit method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29
4.4 Crank-Nicolson method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30
5 Numerical results 32
5.1 Test cases . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32
5.1.1 One-dimensional advection-dispersion model . . . . . . . . . . . . . 32
5.1.2 One-dimensional nonequilibrium advection-dispersion model . . . . . 33
5.2 Numerical results and discussion . . . . . . . . . . . . . . . . . . . . . . . . 33
5.2.1 explicite method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33
6 Conclusion and future works 54
Bibliography 55參考文獻 [1] J. Bear(1988), Dynamics of Fluids in Porous Media, , Dover Publications, New York
[2] J. David Logan, Transport Modeling in Hydrogeochemical Systems, Springer, New
York, 2001.
[3] PHILIP B. BEDIENT,HANADI S. RIFAI, CHARLES J. NEWELL, GROUND WA-
TER CONTAMINATION,Transport and Remediation, Prentice-Hall,Inc., New Jer-
sey, 1994.
[4] NE-ZHENG Sun, MATHEMATICAL MODELING of GROUNDWATER POLLU-
TION, Springer, New York, 1996
[5] MERY P. ANDERSON WILLIAM W.WOESSNER, APPLIED GROUNDWATER
MODELING-Simulation of Flow and Advective Transport, Harcoure Asia Pte Ltd,
Singapore, 2000
[6] VITHAL A. PATEL, Numerical analysis, Harcourt Brace College Publishers,
florida,orlando, 1994
[7] Randall J. LeVeque, Finite Differnce Methods for Ordinary and Partial Differential
Equations, SIAM,Society for Industrial and AppliedMathematics, Philadelphia, 2007
[8] Romuald Szymkiewicz, Numerical Modeling in Open Channel Hydraulics, Springer,
Water Science and Technology 83, poland, 2010
[9] 朱佳仁, 環境流體力學Environmental Fluid Mechanics, 科技圖書, 台北, 2003
55
[10] 楊金忠,蔡樹英,王旭昇, 地下水運動數學模型, 科學出版社, 北京, 2009
[11] 白玉川,顧元棪,邢煥政, 水流泥沙水質數學模型理論與應用, Theory and Application
of Mathematical Model for Water Flow Sediment and Quality, 天津大學出版社, 天
津, 2005
[12] 黃義,張引科, 多相孔隙介質理論及其應用, 科學出版社, 北京, 2009
[13] 許唯臨,楊永全,鄧軍水力學數學模型, 科學出版社, 北京, 2010
[14] 梁昇,黃天福地下水文學, 大學圖書出版社, 台北, 1994
5指導教授 洪盟凱(John M. Hong) 審核日期 2013-8-21 推文 plurk
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