Numerical Models in Groundwater Pollution

1 Introduction.- 2 Basic Equations of Groundwater Flow.- 2.1 Basic Principles of Hydrodynamics.- 2.1.1 Eulerian and Lagrangian Formulations.- 2.1.2 Equilibrium of Forces in Fluid.- 2.1.3 Rate of Deformation.- 2.1.4 Navier-Stokes Equations.- 2.1.5 Potential Flow.- 2.2 Flow Through the Saturated Zone.- 2.2.1 Groundwater and Its Potential.- 2.2.2 Properties of Porous Media.- 2.2.3 The Darcy’s Law.- 2.2.4 Basic Equations of Groundwater Flow.- 2.2.5 Inflows and Outflows.- 2.2.6 Two-Dimensional Case.- 2.2.7 Girinski Potential.- 2.2.8 Basic Boundary and Initial Conditions.- 2.3 Flow Through the Unsaturated Zone.- 2.3.1 Retention Curve.- 2.3.2 Governing Equations of the Unsaturated Flow.- 2.3.3 Boundary and Initial Conditions.- References.- 3 Basic Equations of Transport of Pollutants in Porous Media.- 3.1 Miscible Displacement.- 3.1.1 Fick’s Law, Coefficient of Dispersion.- 3.1.2 Governing Equation of Transport.- 3.1.3 Sorption and Decay of Pollutants.- 3.2 Transport of Immiscible Pollutants.- 3.2.1 General Law of Darcy.- 3.2.2 Basic Equation of Multiphase Flow.- 3.2.3 General Rules of Motion of Insoluble Substances in Porous Media.- References.- 4 Weighted Residuals Method.- 4.1 Basic Terms and Definitions.- 4.1.1 Spaces.- 4.1.2 Operators.- 4.1.3 Function Spaces, Base Functions.- 4.2 Weighted Residuals Method.- 4.2.1 Moments Method.- 4.2.2 Collocation Method.- 4.2.3 Galerkin Method.- 4.2.4 Ritz Method.- 4.3 Weak Solution.- 4.4 Inverse Formulation.- 4.5 Numerical Methods Used in Problems of Groundwater Hydraulics.- References.- 5 Mathematical Models of Groundwater Flow.- 5.1 Groundwater Flow in the Saturated Zone.- 5.1.1 Analytic Solution.- 5.1.2 Finite Differences Method.- 5.1.3 Finite Element Method.- 5.1.4 The Boundary Element Method.- 5.1.5 Dual Reciprocity Method (DRM).- 5.2 Flow in Unsaturated Zone.- 5.2.1 Analytic Solutions.- 5.2.2 Finite Differences Method.- 5.2.3 Finite Element Method.- 5.2.4 Collocation Method.- References.- 6 Mathematical Models of Transport of Miscible Pollutants.- 6.1 Basic Methods.- 6.1.1 Analytic Solution.- 6.1.2 Finite Element Method.- 6.1.3 Dual Reciprocity Method.- 6.1.4 Method of Characteristic Curves.- 6.1.5 Random Walk Method.- 6.2 Equilibrium Sorption.- 6.2.1 Analytic Solution.- 6.2.2 Finite Element Method.- 6.2.3 Particle Methods.- 6.3 Non-Equilibrium Sorption.- 6.3.1 Finite Element Method.- 6.3.2 Random Walk Method.- References.- 7 Comparison of Properties of All the Methods.- 7.1 Groundwater Flow Models.- 7.2 Models of Transport of Pollution.- 8 Examples of the Use of Models in Practice.- 8.1 Models to Determine Groundwater Resources.- 8.2 Models to Assess Different Influences on Groundwater.- 8.2.1 Example of Zilina Locality, Slovakia.- 8.2.2 Example of Ziar Locality, Slovakia.- 8.2.3 Example of SNP Square, Bratislava, Slovakia.- 8.3 Remediation Models.- 8.3.1 Example of Chotebor, Czech Republic.- 8.3.2 Example of Airport Bratislava, Slovakia.- References.- 9 Description of Software Included in This Book.- 9.1 BEFLOW System.- 9.1.1 Program Bemlnp.- 9.1.2 Program BemSolve.- 9.1.3 Program Bemlsol.- 9.1.4 Program BemStream.- 9.1.5 Program BemRaw.- 9.2 System UNSDIS.- 9.2.1 Basic Relations.- 9.2.2 Commands of Program.- 9.3 Examples.- 9.3.1 System BEFLOW.- 9.3.2 Program UNSDIS.- References.