v
Contents
Authors
xi
1 Introduction
1
1.1 Mathematical models 1
1.1.1 Framework of numerical modelling 2
1.1.1.1 Well-posed mathematical models 2
1.1.1.2 Discretization and numerical
solution of mathematical models 3
1.1.1.3 Reliability of mathematical models 4
1.1.2 Development and application of numerical models 5
1.2 Finite differences method 5
1.3 Aim and structure of this book 8
2 Ordinary differential equations
11
2.1 Water storage reservoir management 11
2.1.1 Numerical solutions of the reservoir routing
ordinary differential equation (ODE) 13
2.2 Water quality management in a lagoon 22
3 Common partial differential equations
of computational hydraulics
27
3.1 Classification of partial differential equations 27
3.2 Partial differential equations and characteristic directions 29
3.3 Numerical solutions of typical
partial differential equations 31
3.3.1 Solution of an elliptic partial differential
equation (Laplace equation) 32