8 Computational Modelling in Hydraulic and Coastal Engineering
From this discussion it can be concluded that the numerical solution
is not always achievable, and when obtained, it may be useless. So, careful application of the methods and techniques of numerical analysis and
post-solution checks are required to ensure that the millions of calculations
(numerical solution) executed and the numbers produced by the computer
have physical meaning and are operationally useful.
1.3 AIM AND STRUCTURE OF THIS BOOK
The material contained in this introductory book, Computational Modelling
in Hydraulic and Coastal Engineering, is listed in the following chapters.
• Chapter 1 provides a brief introduction to mathematical modelling
and sets the framework for the numerical treatment of differential
equations with an emphasis on the method of finite differences.
• Chapter 2 describes the numerical treatment of ordinary differential
equations through examples of reservoir storage management and
water quality issues in a semi-enclosed lagoon.
• Chapter 3 provides an introduction to the classification of partial
differential equations into elliptic, parabolic and hyperbolic, and
pre sents simple examples of numerical schemes for solution of the
Laplace equation (elliptic), the diffusion equation (parabolic) and the
wave equation (hyperbolic).
• Chapter 4 presents the fundamentals of flow in pressurized conduits
and delivers solutions for the classical Hardy Cross pipe network
problem and the dynamics of water hammer.
• Chapter 5 deals with steady and unsteady free surface flows in oneand two-dimensional horizontal domains including geophysical stratified flows.
• Chapter 6 provides a brief description of surface gravity waves and
delivers examples of propagation and modulation of those waves in
one- and two-dimensional systems including the phenomenon of harbour basin resonance.
• Chapter 7 describes the mathematical description of groundwater flow
in confined and unconfined aquifers, and provides numerical examples
for one- and two-dimensional applications including saltwater intrusion.
• Chapter 8 deals with problems of mass transport of dissolved or particulate phase in one- or two-dimension domains, and delivers examples of transport of pollutants, sediment and air bubbles by using
Eulerian and Lagrangian solution methodologies.
• Chapter 9 provides a brief description of other major numerical methods such as the weighted residuals, the finite elements method and the
boundary integral method.
From this discussion it can be concluded that the numerical solution
is not always achievable, and when obtained, it may be useless. So, careful application of the methods and techniques of numerical analysis and
post-solution checks are required to ensure that the millions of calculations
(numerical solution) executed and the numbers produced by the computer
have physical meaning and are operationally useful.
1.3 AIM AND STRUCTURE OF THIS BOOK
The material contained in this introductory book, Computational Modelling
in Hydraulic and Coastal Engineering, is listed in the following chapters.
• Chapter 1 provides a brief introduction to mathematical modelling
and sets the framework for the numerical treatment of differential
equations with an emphasis on the method of finite differences.
• Chapter 2 describes the numerical treatment of ordinary differential
equations through examples of reservoir storage management and
water quality issues in a semi-enclosed lagoon.
• Chapter 3 provides an introduction to the classification of partial
differential equations into elliptic, parabolic and hyperbolic, and
pre sents simple examples of numerical schemes for solution of the
Laplace equation (elliptic), the diffusion equation (parabolic) and the
wave equation (hyperbolic).
• Chapter 4 presents the fundamentals of flow in pressurized conduits
and delivers solutions for the classical Hardy Cross pipe network
problem and the dynamics of water hammer.
• Chapter 5 deals with steady and unsteady free surface flows in oneand two-dimensional horizontal domains including geophysical stratified flows.
• Chapter 6 provides a brief description of surface gravity waves and
delivers examples of propagation and modulation of those waves in
one- and two-dimensional systems including the phenomenon of harbour basin resonance.
• Chapter 7 describes the mathematical description of groundwater flow
in confined and unconfined aquifers, and provides numerical examples
for one- and two-dimensional applications including saltwater intrusion.
• Chapter 8 deals with problems of mass transport of dissolved or particulate phase in one- or two-dimension domains, and delivers examples of transport of pollutants, sediment and air bubbles by using
Eulerian and Lagrangian solution methodologies.
• Chapter 9 provides a brief description of other major numerical methods such as the weighted residuals, the finite elements method and the
boundary integral method.