Introduction to Groundwater Modeling : Finite Difference and Finite Element Methods

by Wang; Anderson

• ISBN13: 9780127345857
• ISBN10: 012734585X
• eBook ISBN(s): 9780080571942
• Format: Paperback
• Copyright: 1995-06-23
• Publisher: Elsevier Science

Summary

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.

Table of Contents

Preface	ix
Introduction	1	(18)
Models	1	(5)
Types of Groundwater Models	2	(4)
Physics of Groundwater Flow	6	(7)
Darcy's Law	6	(2)
Hubbert's Force Potential	8	(2)
Darcy's Law in Three Dimensions	10	(1)
Continuity Equation for Steady-State Flow	11	(2)
Laplace's Equation	13	(1)
Boundary Conditions	13	(1)
Regional Groundwater Flow System	14	(5)
Notes and Additional Reading	17	(2)
Finite Differences: Steady-State Flow (Laplace's Equation)	19	(22)
Introduction	19	(2)
Differences for Derivatives
Finite Difference Expression of Laplace's Equation	21	(2)
Example with Dirichlet Boundary Conditions: Region near a Well	23	(1)
Interative Methods	24	(5)
Jacobi Iteration	25	(1)
Gauss-Seidel Iteration	26	(1)
Successive Over Relaxation (SOR)	27	(2)
Gauss-Seidel Computer Program	29	(2)
Boundary Conditions	31	(10)
Notes and Additional Reading	37	(1)
Problems	37	(4)
Finite Differences: Steady-State Flow (Poisson's Equation)	41	(26)
Introduction	41	(1)
Poisson's Equation	41	(2)
Island Recharge	43	(1)
Finite Difference Models	44	(8)
Island Recharge	44	(2)
Well Drawdown (Confined Aquifer)	46	(6)
Unconfined Aquifer with Dupuit Assumptions	52	(10)
Seepage Through a Dam	53	(5)
Well Drawdown (Unconfined Aquifer)	58	(4)
Validity of a Numerical Solution	62	(5)
Notes and Additional Reading	65	(1)
Problems	65	(2)
Finite Differences: Transient Flow	67	(26)
Transient Flow Equation	67	(2)
Explicit Finite Differences Approximation	69	(7)
Validity of the Explicit Solution	70	(1)
Aquifer Response to Sudden Change in Reservoir Level	70	(6)
Implicit Finite Difference Approximation	76	(11)
Well Drawdown (Theis Problem)	79	(8)
Unconfined Aquifer with Dupuit Assumptions	87	(6)
Explicit Approximation	87	(1)
Implicit Approximation	88	(1)
Additional Reading	88	(1)
Problems	89	(4)
Other Solution Methods	93	(20)
Introduction	93	(1)
Matrix Notation	94	(1)
Tridiagonal Matrices	95	(4)
Thomas Algorithm	96	(3)
Direct Solution of Reservoir Problem	99	(1)
Alternating Direction Implicit (ADI) Method	99	(8)
Interative ADI	106	(1)
Prickett-Lonnquist and Trescott-Pinder-Larson Models	107	(2)
Input Data	108	(1)
Calibration and Verification	109	(4)
Calibration	109	(1)
Verification	110	(1)
Notes and Additional Reading	111	(1)
Problems	112	(1)
Finite Elements: Steady-State Flow	113	(38)
Introduction	113	(1)
Galerkin's Method	114	(3)
Integration by Parts	116	(1)
Triangular Elements	117	(4)
Finite Element Mesh	117	(2)
The Archetypal Element	119	(2)
Patch of Elements	121	(1)
Assembly of Conductance Matrix	121	(5)
Element Conductance Matrix	123	(1)
Global Conductance Matrix	124	(2)
Boundary Conditions	126	(2)
Specified Flow	126	(2)
Specified Head	128	(1)
Finite Element Computer Program	128	(6)
Node Specification (Lines 6 to 21)	129	(1)
Global Conductance Matrix (Lines 23 to 50)	129	(4)
Iterative Solution of Equations (Lines 52 to 73)	133	(1)
Region-Near-A-Well Example	134	(4)
Irregular Mesh	134	(4)
Seepage Through A Dam	138	(7)
Self-Consistent Iterative Solution	139	(1)
Computer Program	140	(5)
Poisson's Equation	145	(6)
Computer Program	147	(1)
Notes and Additional Reading	148	(1)
Problems	149	(2)
Finite Elements: Transient Flow	151	(22)
Introduction	151	(1)
Galerkin's Method	152	(1)
Trial Solution	152	(1)
Weighted Residual	153	(1)
Integration by Parts	153	(1)
Rectangular Element	153	(3)
Local and Global Coordinates	156	(1)
Patch of Elements	156	(1)
Assembly of Matrix Differential Equation	156	(4)
Element Matrices	157	(1)
Gaussian Quadrature	158	(1)
Global Matrices	159	(1)
Boundary Conditions	160	(1)
Solving The Matrix Differential Equation	160	(1)
Computer Program for Reservoir Problem	161	(12)
Nodal Coordinates, Initial Conditions, and Boundary Conditions (Lines 11 to 28)	166	(1)
Global Conductance and Storage Matrices (Lines 30 to 71)	167	(1)
Time Stepping (Lines 73 to 114)	167	(3)
Notes and Additional Reading	170	(1)
Problems	170	(3)
Advective-Dispersive Transport	173	(28)
Introduction	173	(2)
Dispersion	175	(6)
Dispersive Flux	177	(1)
Dispersion Coefficient (Uniform Flow Field)	177	(1)
Dispersivity	178	(1)
Dispersion Coefficient (Nonuniform Flow Field)	179	(2)
Solute Transport Equation	181	(4)
Sources, Sinks, and Chemical Reactions	183	(1)
Solving the Governing Equation	183	(2)
Finite Element Example: Solute Dispersion in Uniform Flow Field	185	(16)
Finite Element Theory	186	(2)
Finite Element Computer Program	188	(10)
Additional Reading	198	(1)
Problems	198	(3)
Concluding Remarks	201	(3)
Appendix A Anisotropy and Tensors	204	(5)
A.1 Introduction	204	(1)
A.2 Hydraulic Conductivity Tensor	205	(1)
A.3 Coordinate System Rotation	206	(3)
Appendix B Variational Method	209	(3)
B.1 Introduction	209	(1)
B.2 Minimum Dissipation Principle	209	(2)
B.3 Finite Elements	211	(1)
Appendix C Isoparametric Quadrilateral Elements	212	(7)
C.1 Introduction	212	(1)
C.2 Coordinate Transformation	213	(4)
Element Trial Solution	214	(1)
Transformation of Integrals	214	(3)
C.3 Computer Program Modification	217	(2)
Appendix D Analogies	219	(6)
D.1 Introduction	219	(1)
D.2 Electrical Analogy	219	(3)
D.3 Heat Flow Analogy	222	(1)
D.4 Structural Mechanics Analogy	223	(2)
Glossary of Symbols	225	(2)
References	227	(8)
Index	235