Table of Contents

1. Introduction
2. Water quality in a Lake
2.1. Mathematical Formulation
2.2. Exercises
3. Numerical solution for Box Model
3.1 Principle
3.2 Stability and Accuracy
3.3. Example
3.4. Implicit Method
3.5. Exercises
4. Transport of a Dissolved Substance
4.1. Mathematical Formulation
4.2. Numerical Solution
4.3. Exercises
5. Explicit Finite-Difference Methods
5.1. Two-Level Methods
5.2. The Leap-Frog Method
5.3. The CFL Condition
5.4. Truncation Error
5.5. Wave Propagation
5.6. Exercises
6. Kinematic waves
6.1. Theory
6.2. Example
7. Diffusion
7.1. Groundwater Flow in a Horizontal Layer
7.2. Explicit Finite-Difference Method
7.3. Implicit Finite-Difference Method
7.4. The Thomas Algorithm
7.5. Application
7.6. Exercises
8. Numerical Accuracy for Diffusion Problems
8.1. Fourier Series
8.2. Transfer Function
8.3. Numerical Representation
8.4. Exercises
9. Diffusion Model for Coastline Development
9.1. Mathematical Formulation
9.2. Initial and Boundary Conditions
9.3. Example
9.4. Exercises
10. Consolidation of Soil
10.1. Mathematical Formulation
10.2. Numerical Example
11. Convection-Diffusion
11.1. Transport of a Dissolved Substance
11.2. Numerical Method
11.3. Application
11.4. Exercises
12. Numerical Accuracy for Convection-Diffusion
12.1. Wave Propagation
12.2. Example
12.3. Numerical Diffusion
12.4. Example
12.5. Convection only
12.6. Wiggles
12.7. Exercises
13. Salt intrusion in Estuaries
13.1. Formulation
13.2. Accuracy Mean Concentration
13.3. Accuracy for Tidal Fluctuation
14. Boundary Layers
14.1. Suspended Sediment Transport
14.2. Example
14.3. Boundary-Layer Flows
14.4. Pressure Gradient
14.5. Developing Flow in a River
14.6. Exercises
15. Long Waves
15.1. Simplified Formulation
15.2. Characteristics
15.3. Weakly Reflecting Boundary Conditions
15.4. Example
15.5. Wave Propagation
15.6. Example
15.7. Exercises
16. Numerical Methods for Long Waves
16.1. Leap-Frog Method
16.2. Stability of the Leap-Frog Method
16.3. Example.- 16.4. Implicit Methods
16.5. Numerical Wave Propagation
16.6. Example
16.7. Exercises
17. Long Waves in Two-Dimensional Areas
17.1. Mathematical Formulation
17.2. Wave Propagation and Characteristics Ill
17.3. Boundary Conditions
17.4. Example
18. Finite-Difference Methods for Two-Dimensional Long Waves
18.1. Grids
18.2. Explicit Method
18.3. Alternating-Direction Implicit Method
18.4. Stability
18.5. Wave Propagation
18.6. Example
18.7. Exercises
19. Potential Flow
19.1. Irrotational Flow
19.2. Potential and Stream Function
19.3. Characteristics and Boundary Conditions
19.4. Pressure
19.5. Exercises
20. Finite-Difference Method for Potential Flow
20.1. Difference Equation
20.2. Accuracy
20.3. Example
20.4. Exercises
21. Finite-Element Method
21.1. Principle
21.2. The Galerkin Method
21.3. Boundary Conditions
21.4. Comparison with Finite-Difference Method
21.5. Groundwater Flow
21.6. Exercises
Appendices
Al. Long Waves.- A 1.1. Mathematical Formulation for Rivers.- A 1,2. Mathematical Formulation in Two Dimensions.- A 1.3. Characteristics.- A 1.4. Linearization.- A 1.5. Wave Propagation.
A2. Linear Triangular Finite Elements
References
Subject Index