ISBN: 3-540-66792-X
TITLE: Numerical Models in Groundwater Pollution
AUTHOR: Kovarik, Karel
TOC:

1 Introduction 1
2 Basic Equations of Groundwater Flow 3
2.1 Basic Principles of Hydrodynamics 3
2.1.1 Eulerian and Lagrangian Formulations 3
2.1.2 Equilibrium of Forces in Fluid 6
2.1.3 Rate of Deformation 7
2.1.4 Navier-Stokes Equations 9
2.1.5 Potential Flow 10
2.2 Flow Through the Saturated Zone 12
2.2.1 Groundwater and Its Potential 13
2.2.2 Properties of Porous Media 14
2.2.3 The Darcy's Law 16
2.2.4 Basic Equations of Groundwater Flow 19
2.2.5 Inflows and Outflows 22
2.2.6 Two-Dimensional Case 23
2.2.7 Girinski Potential 25
2.2.8 Basic Boundary and Initial Conditions 27
2.3 Flow Through the Unsaturated Zone 28
2.3.1 Retention Curve 28
2.3.2 Governing Equations of the Unsaturated Flow 30
2.3.3 Boundary and Initial Conditions 32
References 33
3 Basic Equations of Transport of Pollutants in Porous Media 35
3.1 Miscible Displacement 35
3.1.1 Fick's Law, Coefficient of Dispersion 36
3.1.2 Governing Equation of Transport 39
3.1.3 Sorption and Decay of Pollutants 41
3.2 Transport of Immiscible Pollutants 45
3.2.1 General Law of Darcy 45
3.2.2 Basic Equation of Multiphase Flow 46
3.2.3 General Rules of Motion of Insoluble Substances in Porous Media 47
References 48
4 Weighted Residuals Method 49
4.1 Basic Terms and Definitions 49
4.1.1 Spaces 49
4.1.2 Operators 50
4.1.3 Function Spaces, Base Functions 50
4.2 Weighted Residuals Method 52
4.2.1 Moments Method 53
4.2.2 Collocation Method 54
4.2.3 Galerkin Method 54
4.2.4 Ritz Method 55
4.3 Weak Solution 55
4.4 Inverse Formulation 57
4.5 Numerical Methods Used in Problems of Groundwater Hydraulics 58
References 60
5 Mathematical Models of Groundwater Flow 61
5.1 Groundwater Flow in the Saturated Zone 61
5.1.1 Analytic Solution 61
5.1.2 Finite Differences Method 64
5.1.3 Finite Element Method 69
5.1.4 The Boundary Element Method 84
5.1.5 Dual Reciprocity Method (DRM) 100
5.2 Flow in Unsaturated Zone 101
5.2.1 Analytic Solutions 102
5.2.2 Finite Differences Method 102
5.2.3 Finite Element Method 103
5.2.4 Collocation Method 106
References 107
6 Mathematical Models of Transport of Miscible Pollutants 109
6.1 Basic Methods 110
6.1.1 Analytic Solution 111
6.1.2 Finite Element Method 111
6.1.3 Dual Reciprocity Method 113
6.1.4 Method of Characteristic Curves 116
6.1.5 Random Walk Method 117
6.2 Equilibrium Sorption 119
6.2.1 Analytic Solution 120
6.2.2 Finite Element Method 120
6.2.3 Particle Methods 121
6.3 Non-Equilibrium Sorption 122
6.3.1 Finite Element Method 122
6.3.2 Random Walk Method 123
References 124
7 Comparison of Properties of All the Methods 125
7.1 Groundwater Flow Models 125
7.2 Models of Transport of Pollution 129
8 Examples of the Use of Models in Practice 131
8.1 Models to Determine Groundwater Resources 131
8.2 Models to Assess Different Influences on Groundwater 131
8.2.1 Example of Zilina Locality, Slovakia 131
8.2.2 Example of Ziar Locality, Slovakia 138
8.2.3 Example of SNP Square, Bratislava, Slovakia 145
8.3 Remediation Models 153
8.3.1 Example of Chotebor, Czech Republic 153
8.3.2 Example of Airport Bratislava, Slovakia 164
References 174
9 Description of Software Included in This Book 175
9.1 BEFLOW System 175
9.1.1 Program BemInp 177
9.1.2 Program BemSolve 186
9.1.3 Program BemIsol 193
9.1.4 Program BemStream 196
9.1.5 Program BemRaw 201
9.2 System UNSDIS 207
9.2.1 Basic Relations 207
9.2.2 Commands of Program 209
9.3 Examples 212
9.3.1 System BEFLOW 212
9.3.2 Program UNSDIS 217
References 218
Subject Index 219
END
