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Groundwater Modeling by the Finite Element Method

Groundwater Modeling by the Finite Element Method

Jonathan Istok

ISBN: 978-1-118-66554-1

Mar 2013, American Geophysical Union

495 pages

Select type: O-Book

Description

Published by the American Geophysical Union as part of the Water Resources Monograph Series, Volume 13.

The finite element method is now widely used to solve a variety of important problems in the field of groundwater hydrology. Thus a clear understanding of the method is essential to scientists and engineers working in this field. The goal of this book is to provide the reader with the basic skills needed to use the finite element method to solve "real-world" problems. Examples are used throughout the text to illustrate each step in the solution process.

Preface xiii

PART ONE BASIC CONCEPTS

Chapter I INTRODUCTION  3

Chapter 2 STEP 1- DISCRETIZE THE PROBLEM DOMAIN  13

Chapter 3 STEP 2: DERIVE THE APPROXIMATING EQUATIONS  30

Chapter 4 STEP 3: DEVELOP SYSTEM OF EQUATIONS 80

Chapter 5 STEP 4: SOLVE SYSTEM OF EQUATIONS  176

Chapter 6 STEP 5: CALCULATE REQUIRED ELEMENT RESULTANTS 226

PART TWO COMPUTER IMPLEMENTATION 

Chapter 7 FINFFE ELEMENT COMPUTER PROGRAMS 255

Chapter 8 SUBROUTINE NODES 303

Chapter 9 SUBROUTINE ELEMENT 311

Chapter 10 SUBROUTINE MATERIAL 318

Chapter 11 SUBROUTINE BOUND 325

Chapter 12 SUBROUTINE ASMBK  331

Chapter 13 SUBROUTINES DECOMP AND SOLVE  363

Chapter 14 SUBROUTINE VELOCITY  371

Chapter 15 SUBROUTINE DUMP  393

Chapter 16 SUBROUTINE INITIAL  400

Chapter 17 SUBROUTINE ASMBKC  406

Chapter 18 SUBROUTINE RHS  420

Chapter 19 SUBROUTINE ASMBAD  423

PART THREE APPLICATIONS

Chapter 20 MODELING REGIONAL GROUNDWATER FLOW  445

Chapter 21 MODELING SOLUTION TRANSPORT  454

APPENDICES

Appendix I Derivation of Equations of Steady-State Groundwater  Flow  458

Appendix II Derivation of Equations of Transient Groundwater Flow  464

Appendix III Derivation of Equationos of Solute Transport  469

Appendix IV Concepts from Linear Algebra used in the Finite Element Method  478

Appendix V Properties of Selected Aquifer Materials  485

REFERENCES  487

Index  493