The Boundary Element Method for Groundwater Flow

1 Porous Media Flows.- 1.1 Introduction.- 1.2 Application of Continuum Mechanics to Porous Media.- 1.3 Equation Describing the Porous Media Flow.- 1.4 The Boundary Conditions.- 2 The Laplace Equation.- 2.1 Introduction.- 2.2 The Mathematical Model.- 2.3 Mathematical Aspects of the Laplace Equation.- 2.4 Solution of the Laplace Equation.- 3 Introduction to the Boundary Element Method.- 3.1 Introduction.- 3.2 Governing Equation.- 3.3 The Basic Equation of the Boundary Element Method.- 3.4 The Weighting Function.- 3.5 Analysis of the Integrals.- 3.6 Discretization of the Problem.- 3.7 Special Problems.- 3.8 Conclusion.- 4 Numerical Integration.- 4.1 Introduction.- 4.2 Regular Integration.- 4.3 Singular Integration of Geij.- 4.4 Singular Integration of Heij.- 4.5 Conclusions.- 5 Numerical Aspects of the Boundary Element Method.- 5.1 Introduction.- 5.2 Comparison of the Integration Methods.- 5.3 Study of the Discretization.- 5.4 Sensitivity of the Results to the Variations of Geometry.- 5.5 Conclusions.- 6 Division of the Domain into Sub-regions.- 6.1 Introduction.- 6.2 Discretization of the Integrals.- 6.3 The Linear System.- 6.4 Earlier Solutions.- 6.5 Analysis of the Numerical Problem.- 6.6 The Additional Equation.- 6.7 Summary of the Theory.- 6.8 Applications.- 6.9 Special Interfaces.- 6.10 Conclusions.- 7 Steady State Flow Through Porous Media.- 7.1 Introduction.- 7.2 Iterative Determination of the Free Surface Position.- 7.3 Applications.- 7.4 Conclusions.- 8 Unsteady Flow Through Porous Media.- 8.1 Introduction.- 8.2 Iterative Determination of the Free Surface Position.- 8.3 Applications.- 8.4 Choice of the Discretization.- 8.5 Conclusions.- 9 Infiltration Problems.- 9.1 Introduction.- 9.2 Previous Solutions.- 9.3 Iterative Determination of the Free Surface Position.-9.4 Computational Examples.- 9.5 Conclusions.- 10 Conclusions.- 11 References.- Acknowledgments.