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In this book the application of the boundary element method
to the solution of the Laplace equation is examined. This
equation is of fundamental importance in engineering and
science as it describes different types of phenomena, inclu-
ding the groundwater flow applications highlighted in this
book. Special subjects such as numerical integration, subdi-
visionof the domain into regions and other computational
aspects are discussed in detail in the first chapters. To
demonstrate the accuracy and efficiency of the boundary ele-
ment method, results obtained when solving the Laplace equa-
tion have been compared against known analytical solutions.
Other chapters deal with problems such as steady and unstea-
dy flow in addition to infiltration problems. The applica-
tions demonstrate that the boundary element method provides
a powerful solution technique which can be effectively ap-
plied to solve this type of problem.
List of contents
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.
