Mathematical Analysis of Groundwater Resources

Mathematical Analysis of Groundwater Resources focuses on groundwater flow. The book first discusses the scope of the study, definition of terms, and mathematical preliminaries. The text examines the equations of groundwater flow. Continuum concepts; flux and pore velocities; Darcy's Law for Anisotropic Aquifers; Conservation of Mass equations; and boundary conditions are discussed. The book also underscores the formulation of boundary-value problems. Regional problems, confined flow problems, sea water intrusion problems, and free surface flows are discussed. The text also looks at the approximate solution of boundary-value problems, inverse problems, and groundwater pollution. The book then presents the exact solutions of steady-flow problems. Problem formulations; analytic coordinate transformations; analytic functions of a complex variable; applications of the Schwarz-Christoffel transformation; and superposition of solutions are described. The text also discusses the exact solution of unsteady problems. The Laplace transform, groundwater recharge problems, well storage effect, and two well recovery problems are discussed. The book is a good source of data for researchers who are interested in groundwater flow.

Chapter I. Introduction

1. The Scope of Study

2. Definitions of Terms

3. Mathematical Preliminaries

Chapter II. The Equations of Groundwater Flow

4. Continuum Concepts

5. Flux and Pore Velocities

6. Darcy's Law

7. Darcy's Law for Anisotropic Aquifers

8. Conservation of Mass Equations

9. Boundary Conditions

Chapter III. The Formulation of Boundary-Value Problems

10. Regional Problems

11. A Confined Flow Problem

12. A Sea Water Intrusion Problem

13. Free Surface Flows

Chapter IV. The Approximate Solution of Boundary-Value Problems

14. The Finite-Difference Method

15. Solution of the Finite-Difference Equations

16. Computer Coding

17. Computer Program Modifications

18. Unsteady Flow Solutions

19. Computer Coding

20. Other Numerical Techniques

21. Hele-Shaw Experiments

Chapter V. The Inverse Problem

22. Transmissivity Calculations in Steady Flow

23. Disturbance Speeds in Groundwater Flow

24. Pump Tests

25. Analysis of Pump Test Data

26. Some Additional Inverse Methods

Chapter VI. Groundwater Pollution

27. Diffusion and Dispersion

28. The Dispersion Tensor

29. Pollution Sources in Uniform Flow

30. Series Expansions of the Well Function for Leaky Aquifers

31. Pollution Calculations in Non-Uniform Flow

Chapter VII. The Exact Solution of Steady-Flow Problems

32. Problem Formulations

33. Analytic Functions of a Complex Variable

34. Some Basic Potential Functions

35. Superposition of Solutions

36. Analytic Coordinate Transformations

37. The Schwarz-Christoffel Transformation

38. Applications of the Schwarz-Christoffel Transformation

39. The Inverse Velocity Hydro-graph

Chapter VIII. The Exact Solution of Unsteady Problems

40. The Laplace Transform

41. Some One-Dimensional Examples

42. A Groundwater Recharge Problem

43. The Well Storage Effect

44. Two Well Recovery Problems

Appendix

I. Trigonometric and Hyperbolic Functions with Complex Arguments

II. The Numerical Calculation of Singular Integrals

III. Worked Example Problems

IV. Notation

Index