地下水污染物迁移转化模型及数值解_Parts 3
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地下水污染控制与修复——王明玉
SCALE OF MODELING AT LARGE-SCALE COMPLEX SITES-----continued
•The site subsurface is often quite complex, requiring extensive characterization prior to development of a conceptual model •The database housing all associated data may grow to several gigabytes in size and may be accessed by parties from all over the country, from Project Scientist to lay persons
第三部分： 第三部分：地下水污染物迁移转化模型与数值解 地下水数值模拟简介 流体流动基本方程与溶质运移基本方程 数值方法简介
地下水污染控制与修复——王明玉
∂ ∂H ∂ ∂H ∂H ( K xx M ) + ( K yy M ) + ε = µe ∂x ∂x ∂y ∂y ∂t
∂ ∂H ∂ ∂H ∂H ( K xx H ) + ( K yy H ) + ε = µd ∂x ∂x ∂y ∂y ∂t
地下水污染控制与修复——王明玉
有限元方法主要步骤
对求解区域进行单元剖分 单元上函数的插值逼近 生成单元上的线性代数方程组 合成所有单元上的方程组，生成全 解域上的线性代数方程组 • 大稀疏阵求解 • • • •
地下水污染控制与修复——王明玉
边界条件: 1. 指定浓度（ 指定浓度（Dirichlet条件）； 条件）； 2. 指定浓度梯度或弥散通量 （Neumann条件）； 条件）； 3.指定浓度及浓度梯度－－ 指定浓度及浓度梯度－－总通 －－总通 量（Cauchy条件) 。
• 2维情形
网格剖分 x-t上平面
t
nτ
网格节点
2τ
τ
-2h -h 0 h 2h mh
x
n um = u ( xm , tn )
x = xm = m∆x = mh
t = tn = n∆t = nt
地下水污染控制与修复——王明玉
有限差分方法
• 有限差分格式的收敛性 时间步长和空间步长无限缩小时， 时间步长和空间步长无限缩小时， 差分格式的解是否逼近到微分方程 的解 • 有限差分格式的稳定性 在利用有限差分格式按时间逐层计 算时， 算时，误差的影响是否越来越大
地下水污染控制与修复——王明玉
有限元方法
有限元问题的提出 • 有限元离散化的思想早在20世纪40年代 就已被提出（ 就已被提出（R.Couraut，1943），并在 ），并在 50年代被西方的一些结构工程师所采用。 年代被西方的一些结构工程师所采用。 • 冯康院士曾归纳其要点： 冯康院士曾归纳其要点： “化整为零、 化整为零、裁弯取直、 裁弯取直、以简驭繁、 以简驭繁、化 难为易” 难为易” • 基础原理是变分原理及剖分插值。 基础原理是变分原理及剖分插值。
基本定律:质量守恒 基本解方法: 有限差分与有限元 计算实现与结果可视化工具:计算机
地下水污染控制与修复——王明玉
数值模拟方法的应用步骤:
Data collection and database setup (数据搜集与数据 库建立) Conceptual model (概念模型) Model selection (模型选取) Model calibration (模型识别) Model validation(模型验证) Sensitivity analysis (灵敏度分析) Predictive uncertainty(模型预测不确定性分析) Model application (模型应用) Model refinement (模型改进)
地下水污染控制与修复——王明玉
PRIMARY ISSUES OF CONCERN AT LARGE AND COMPLEX SITES
Data availability – How many sampling points are there? For how long? Data spatial distribution – Where are they located relative to the plume / source? Data quality / data management – Where is the data housed? Who uses it? Characterization and conceptualization of Site Conditions - How can they be represented conceptually?
地下水污染控制与修复——王明玉
SCIENTIFIC / TECHNICAL FACTORS TO BE CONSIDERED
•Calibration of a model: Models utilized to simulate groundwater flow and transport must be carefully and comprehensively calibrated. •Validation of a model: Models used to simulate groundwater flow and transport at large-scale and complex sites must be thoroughly tested and validated. •Groundwater and subsurface data: Should be collected using the best available sampling technology and guidelines. •Data / parameter representative scales: parameters obtained from pumping tests, for example, can represent a large area, while those obtained from slug tests represent a much smaller area. 地下水污染控制与修复——王明玉
地下水污染控制与修复——王明玉
地下水污染控制与修复——王明玉
地下水污染控制与修复——王明玉
溶质运移转化偏微分方程
地下wk.baidu.com污染控制与修复——王明玉
地下水污染控制与修复——王明玉
where qs′ = ∂θ /∂t is the rate of change in transient groundwater storage (unit, T-1).
地下水污染控制与修复——王明玉
据Fick 第一定律，通过单位截面积溶质总 量：
地下水污染控制与修复——王明玉
微分方程数值解法
地下水污染控制与修复——王明玉
微分方程数值解法
当今流行两类方法 • 有限差分方法
主要集中在依赖于时间的问题
• 有限元方法
侧重于定态问题
地下水污染控制与修复——王明玉
有限差分方法
地下水污染控制与修复——王明玉
National Academy of Sciences:
Thus, when models form the basis for decision-making, uncertainty will be an inescapable component of environmental management and regulation. A key consideration in any modeling process is whether the model has undergone sufficient development and testing to address the problem being analyzed in a sufficiently meaningful manner.
地下水污染控制与修复——王明玉
National Academy of Sciences:
When carefully developed and supported by field data, models can be effective tools for understanding complex phenomena and for making informed predictions. However, model results are always subject to some degree of uncertainty due to limitations in field data and incomplete knowledge of natural processes.
地下水污染控制与修复——王明玉
PRIMARY ISSUES OF CONCERN AT LARGE AND COMPLEX SITES-----Continued
These concerns encompass 3 main areas of scientific discipline: Modeling – Data simulation / prediction of scenarios / model adaptability Database – Information / data management / data storage and retrieval GIS – Spatial distribution / sample management, interpretation and presentation Ideally, all 3 disciplines should be invoked and a Team of experts from all 3 disciplines should be assigned. The Team approach will greatly facilitate addressing the Site objectives and concerns in a UNIFIED and CONSISTENT MANNER.
地下水污染控制与修复——王明玉
有限差分与有限元数值解法的 主要差异： 主要差异： （1）网格刨分灵活性方面 （2）质量守恒方面
地下水污染控制与修复——王明玉
地下水模拟建模过程与方法
地下水污染控制与修复——王明玉
Introduction to Modeling Approaches
地下水污染控制与修复——王明玉
remediation? Natural attenuation? Is the plume growing, shrinking or stable?
•Future modeling needs – Where is the
plume going? Is the treatment system working? $$$$$ ?
地下水污染控制与修复——王明玉
SCALE OF MODELING AT LARGELARGE-SCALE COMPLEX SITES
Sites are usually large (>100 acres) in physical size with many compounds impacting groundwater and soil •Time scales could be rather long for modeling site natural or engineered remediation, e.g., more than 100 years •Modeling tasks can be quite complex and involved from the start. Multi-level, 3-D transient flow and transport models are common. These models usually have extensive data needs for development and calibration
地下水污染控制与修复——王明玉
PRIMARY ISSUES OF CONCERN AT LARGE AND COMPLEX SITES---Continued
•Best (optimal) model to use – What do
you need to simulate?
•Scope / Goal of the Project – Active
SCALE OF MODELING AT LARGE-SCALE COMPLEX SITES-----continued
•The site subsurface is often quite complex, requiring extensive characterization prior to development of a conceptual model •The database housing all associated data may grow to several gigabytes in size and may be accessed by parties from all over the country, from Project Scientist to lay persons
第三部分： 第三部分：地下水污染物迁移转化模型与数值解 地下水数值模拟简介 流体流动基本方程与溶质运移基本方程 数值方法简介
地下水污染控制与修复——王明玉
∂ ∂H ∂ ∂H ∂H ( K xx M ) + ( K yy M ) + ε = µe ∂x ∂x ∂y ∂y ∂t
∂ ∂H ∂ ∂H ∂H ( K xx H ) + ( K yy H ) + ε = µd ∂x ∂x ∂y ∂y ∂t
地下水污染控制与修复——王明玉
有限元方法主要步骤
对求解区域进行单元剖分 单元上函数的插值逼近 生成单元上的线性代数方程组 合成所有单元上的方程组，生成全 解域上的线性代数方程组 • 大稀疏阵求解 • • • •
地下水污染控制与修复——王明玉
边界条件: 1. 指定浓度（ 指定浓度（Dirichlet条件）； 条件）； 2. 指定浓度梯度或弥散通量 （Neumann条件）； 条件）； 3.指定浓度及浓度梯度－－ 指定浓度及浓度梯度－－总通 －－总通 量（Cauchy条件) 。
• 2维情形
网格剖分 x-t上平面
t
nτ
网格节点
2τ
τ
-2h -h 0 h 2h mh
x
n um = u ( xm , tn )
x = xm = m∆x = mh
t = tn = n∆t = nt
地下水污染控制与修复——王明玉
有限差分方法
• 有限差分格式的收敛性 时间步长和空间步长无限缩小时， 时间步长和空间步长无限缩小时， 差分格式的解是否逼近到微分方程 的解 • 有限差分格式的稳定性 在利用有限差分格式按时间逐层计 算时， 算时，误差的影响是否越来越大
地下水污染控制与修复——王明玉
有限元方法
有限元问题的提出 • 有限元离散化的思想早在20世纪40年代 就已被提出（ 就已被提出（R.Couraut，1943），并在 ），并在 50年代被西方的一些结构工程师所采用。 年代被西方的一些结构工程师所采用。 • 冯康院士曾归纳其要点： 冯康院士曾归纳其要点： “化整为零、 化整为零、裁弯取直、 裁弯取直、以简驭繁、 以简驭繁、化 难为易” 难为易” • 基础原理是变分原理及剖分插值。 基础原理是变分原理及剖分插值。
基本定律:质量守恒 基本解方法: 有限差分与有限元 计算实现与结果可视化工具:计算机
地下水污染控制与修复——王明玉
数值模拟方法的应用步骤:
Data collection and database setup (数据搜集与数据 库建立) Conceptual model (概念模型) Model selection (模型选取) Model calibration (模型识别) Model validation(模型验证) Sensitivity analysis (灵敏度分析) Predictive uncertainty(模型预测不确定性分析) Model application (模型应用) Model refinement (模型改进)
地下水污染控制与修复——王明玉
PRIMARY ISSUES OF CONCERN AT LARGE AND COMPLEX SITES
Data availability – How many sampling points are there? For how long? Data spatial distribution – Where are they located relative to the plume / source? Data quality / data management – Where is the data housed? Who uses it? Characterization and conceptualization of Site Conditions - How can they be represented conceptually?
地下水污染控制与修复——王明玉
SCIENTIFIC / TECHNICAL FACTORS TO BE CONSIDERED
•Calibration of a model: Models utilized to simulate groundwater flow and transport must be carefully and comprehensively calibrated. •Validation of a model: Models used to simulate groundwater flow and transport at large-scale and complex sites must be thoroughly tested and validated. •Groundwater and subsurface data: Should be collected using the best available sampling technology and guidelines. •Data / parameter representative scales: parameters obtained from pumping tests, for example, can represent a large area, while those obtained from slug tests represent a much smaller area. 地下水污染控制与修复——王明玉
地下水污染控制与修复——王明玉
地下水污染控制与修复——王明玉
地下水污染控制与修复——王明玉
溶质运移转化偏微分方程
地下wk.baidu.com污染控制与修复——王明玉
地下水污染控制与修复——王明玉
where qs′ = ∂θ /∂t is the rate of change in transient groundwater storage (unit, T-1).
地下水污染控制与修复——王明玉
据Fick 第一定律，通过单位截面积溶质总 量：
地下水污染控制与修复——王明玉
微分方程数值解法
地下水污染控制与修复——王明玉
微分方程数值解法
当今流行两类方法 • 有限差分方法
主要集中在依赖于时间的问题
• 有限元方法
侧重于定态问题
地下水污染控制与修复——王明玉
有限差分方法
地下水污染控制与修复——王明玉
National Academy of Sciences:
Thus, when models form the basis for decision-making, uncertainty will be an inescapable component of environmental management and regulation. A key consideration in any modeling process is whether the model has undergone sufficient development and testing to address the problem being analyzed in a sufficiently meaningful manner.
地下水污染控制与修复——王明玉
National Academy of Sciences:
When carefully developed and supported by field data, models can be effective tools for understanding complex phenomena and for making informed predictions. However, model results are always subject to some degree of uncertainty due to limitations in field data and incomplete knowledge of natural processes.
地下水污染控制与修复——王明玉
PRIMARY ISSUES OF CONCERN AT LARGE AND COMPLEX SITES-----Continued
These concerns encompass 3 main areas of scientific discipline: Modeling – Data simulation / prediction of scenarios / model adaptability Database – Information / data management / data storage and retrieval GIS – Spatial distribution / sample management, interpretation and presentation Ideally, all 3 disciplines should be invoked and a Team of experts from all 3 disciplines should be assigned. The Team approach will greatly facilitate addressing the Site objectives and concerns in a UNIFIED and CONSISTENT MANNER.
地下水污染控制与修复——王明玉
有限差分与有限元数值解法的 主要差异： 主要差异： （1）网格刨分灵活性方面 （2）质量守恒方面
地下水污染控制与修复——王明玉
地下水模拟建模过程与方法
地下水污染控制与修复——王明玉
Introduction to Modeling Approaches
地下水污染控制与修复——王明玉
remediation? Natural attenuation? Is the plume growing, shrinking or stable?
•Future modeling needs – Where is the
plume going? Is the treatment system working? $$$$$ ?
地下水污染控制与修复——王明玉
SCALE OF MODELING AT LARGELARGE-SCALE COMPLEX SITES
Sites are usually large (>100 acres) in physical size with many compounds impacting groundwater and soil •Time scales could be rather long for modeling site natural or engineered remediation, e.g., more than 100 years •Modeling tasks can be quite complex and involved from the start. Multi-level, 3-D transient flow and transport models are common. These models usually have extensive data needs for development and calibration
地下水污染控制与修复——王明玉
PRIMARY ISSUES OF CONCERN AT LARGE AND COMPLEX SITES---Continued
•Best (optimal) model to use – What do
you need to simulate?
•Scope / Goal of the Project – Active