The Boundary Element Method for Groundwater Flow

ISBN-13: 9783540544074 / Angielski / Miękka / 1991 / 120 str.

E. K. Bruch; Erwin K. Bruch

Opis

This monograph examines the application of the boundary element method to the solution of the Laplace equation, with specific reference to its importance in engineering and science. Focusing on groundwater flow applications, the text also covers infiltration problems and steady flow.

Spis treści

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.