Mathematical models are powerful tools used in the prediction of pollutant movement. This book discusses the Finite Element Method (FEM) and Boundary Element Method (BEM), and takes a look at the advantages of these methods in groundwater hydrology. The combination of the BEM and the random-walk particle tracking method is also presented. The book includes computer programs, source code, and examples developed on the basis of the theoretical backgrounds of these methods. These Visual C++ programs are compatible with the Windows platform.
Mathematical models are powerful tools used in the prediction of pollutant movement. This book discusses the Finite Element Method (FEM) and Boundary Element Method (BEM), and takes a look at the advantages of these methods in groundwater hydrology. The combination of the BEM and the random-walk particle tracking method is also presented. The book includes computer programs, source code, and examples developed on the basis of the theoretical backgrounds of these methods. These Visual C++ programs are compatible with the Windows platform.
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.
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.
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