Introduction to Groundwater Modeling - 1st Edition - ISBN: 9780127345857, 9780080571942

Introduction to Groundwater Modeling

1st Edition

Finite Difference and Finite Element Methods

Authors: Herbert Wang Mary Anderson
eBook ISBN: 9780080571942
Imprint: Academic Press
Published Date: 23rd June 1995
Page Count: 237
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The dramatic advances in the efficiency of digital computers during the past decade have provided hydrologists with a powerful tool for numerical modeling of groundwater systems. Introduction to Groundwater Modeling presents a broad, comprehensive overview of the fundamental concepts and applications of computerized groundwater modeling.

The book covers both finite difference and finite element methods and includes practical sample programs that demonstrate theoretical points described in the text. Each chapter is followed by problems, notes, and references to additional information. This volume will be indispensable to students in introductory groundwater modeling courses as well as to groundwater professionals wishing to gain a complete introduction to this vital subject.

Key Features

  • Systematic exposition of the basic ideas and results of Hilbert space theory and functional analysis
  • Great variety of applications that are not available in comparable books
  • Different approach to the Lebesgue integral, which makes the theory easier, more intuitive, and more accessible to undergraduate students


Graduate students in groundwater hydrology courses

Table of Contents

Introduction: Models. Physics of Groundwater Flow. Laplaces Equation. Regional Groundwater Flow System. Finite Differences: Steady State Flow (Laplaces Equation): Differences for Derivatives. Iterative Methods. Gauss–Seidel Computer Program. Boundary Conditions. Finite Differences: Steady State Flow (Poissons Equation): Poissons Equation. Island Recharge. Finite Difference Models. Unconfined Aquifer with Dupuit Assumptions. Validity of a Numerical Solution. Finite Differences: Transient Flow: Transient Flow Equation. Explicit Finite Difference Approximation. Implicit Finite Difference Approximation. Unconfined Aquifer with Dupuit Assumptions. Other Solution Methods. Matrix Notation. Tridiagonal Matrices. Alternating Direction Implicit (ADI) Method. Prickett–Lonnquist and Trescott–Pinder–Larson Models. Calibration and Verification. Finite Elements: Steady-State Flow: Galerkins Method. Triangular Elements. Assembly of ConductanceMatrix. Boundary Conditions. Finite Element Computer Program. Region-Near-a-Well Example. Seepage through a Dam. Poissons Equation. Finite Elements: Transient Flow: Galerkins Method. Rectangular Element. Assembly of Matrix Differential Equation. Solving the Matrix Differential Equation. Computer Program for Reservoir Problem. Advective–Dispersive Transport: Dispersion. Solute Transport Equation. Finite Element Example: Solute Dispersion in Uniform Flow Field. Concluding Remarks. Appendixes: Anisotropy and Tensors. Variational Method. Isoparametric Quadrilateral Elements. Analogies. Glossary of Symbols. References. Index.


No. of pages:
© Academic Press 1995
Academic Press
eBook ISBN:

About the Author

Herbert Wang

Affiliations and Expertise

University of Wisconsin, Madison

Mary Anderson

Affiliations and Expertise

University of Wisconsin-Madison, USA


"It can be readily understood by all newcomers to numerical methods requiring only basic mathematical techniques....Short FORTRAN-computer programs for almost every a great advantage of the book....This book is as good as a complete and very detailed university course." --JOURNAL OF GEOPHYSICS

"Very timely....The authors have succeeded in avoiding complex formulated expressions without losing mathematical consistency....This introductory textbook...will be very useful in the development of college hydrogeology courses." --GROUNDWATER MODELING NEWSLETTER

"A clear, concise little volume on a subject that has needed such a treatment. It provides the best introduction to date on the most important tool of groundwater hydrology, the computer model...." --CHOICE

"This well-written, soft-bound book is a very good treatment of numerical methods applied to modeling ground water flow....The book will also be valuable as a reference for practitioners working in the area of ground water flow. I personally would buy the book for my own library." --WATER RESOURCES BULLETIN

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