NUMERICAL METHODS AND OPTIMISATION
IN ENVIRONMENTAL ENGINEERING
PROPOSAL FOR MODULE CHARACTERISTICS
Dr. CHRISTOPHER KOUTITAS
Scope of the module
• To introduce to the notion of computational models and operational
software .
• To point out the importance of models quality control
• To present the basic methods of numerical analysis for the solution of ODE
and PDE relevant to environmental sciences
• To present the procedures towards the solution of most common
equations in Environmental sciences
• To refer to commonly used and available commercial or open
environmental software packages
• To introduce to the basic optimisation notions and problems and present
the classical and modern optimisation techniques
• To gain experience on using optimisation techniques for decision making
in environmental management issues
• COURSE DURATION 33 HRS
Module contents
• Chapter 1. Modelling basics
Simplifying assumptions, parameterisations and model synthesis
Models categorisation
Models quality control , pre-processing and post processing
From models to computer packages
• Chapter 2. Methods and techniques of numerical analysis
Fundamentals of FD method
Convergence, stability, implicit and explicit schemes
Initial and boundary conditions
Monte Carlo methods, particles in place of the continuum
• Chapter 3. Solution of fundamental ODE and PDE in environmental
sciences
Module contents
Solution of Volterra equation, (nonlinear ODE)
Solution of the transport equation (advection diffusion)
Non steady flows and long waves equation
Water quality equation (one or more reacting constituents)
• Chapter 4. Application to water problems
Flood propagation and sediments transport
Water quality control
Oil slick transport
• Chapter 5. Application to air pollution
Box and Gauss models
Emission and fate of pollutants in lower atmosphere
• Chapter 6. Application to biological problems (population dynamics)
Module contents
• Chapter 7. Optimisation methods
Objective function, constrained and unconstrained optimisation
Linear problems, Linear programming, Lagrange multipliers, Method of
Steepest Descent
Modern heuristic methods (Genetic algorithms, Particle swarm
optimisation)
Application to decision support for environmental management, selected
case studies
• Chapter 8. Available software packages
Critical presentation of CEDES, WASP6, OSPM, AFTOX, POLYMATH etc
The lecturer
PhD in Sciences or Engineering with experience
in CFD
• Environmental Engineering
• Civil Engineering
• Chemical Engineering
• Applied Mathematics
• Biology or Physics with strong mathematical
background
Bibliography
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Elements of Computational Hydraulics, C. Koutitas, Chapman & Hall 1988
Introduction to Environmental Modelling, J. Smith. Oxford 2007
Population Ecology of Individuals Lomnicki, Princeton U., 1988
Environmental Modelling Software and Decision Support , A. Jakeman,
2008
• Fundamentals of Air Pollution, from processes to modelling, B. Sportisse,
Springer 2009
• Engineering optimization, An introduction with meta-heuristic
applications, Xin-She Yang, Wiley, 2010