Computational Methods Applied to Environmental Modelling

Recommended Prerequisites

Basic knowledge of mathematical analysis, linear algebra and numerical methods

Teaching Methods

The lectures will be of traditional format, which is essentially driven by the exposure of the subjects in Powerpoint slides to introduce fundamental concepts and discuss in detail the contents and their applications in everyday engineering. Key concepts and their applications will be explained and illustrated with many examples. Exemplary computations done “by hand” help to follow and understand the numerical methods.

Problem-based computer laboratory: introduce MATLAB to students and enable them to apply MATLAB to create computational code for solving engineering problems.

Learning Outcomes

The goal of this course is twofold: (a) to provide students of different formations which usually apply for this PhD programme with the knowledge of essential concepts and an unifying basis of the most common numerical methods used to solve engineering problems when no analytical solution exists;  (b) to provide the theoretical background and working knowledge of computational methods, including implementing them efficiently in Matlab environment, indispensable for solving a variety of mathematical models based on differential equations arising in many areas of engineering, with more emphasis on environmental modelling.

At the end of the course, the students should be able to:

- Understand the most common numerical techniques, emphasizing practical application and limits of their appropriate use.

- Apply mathematical models to solve problems in environmental engineering and understand the discretisation of governing differential equations by finite difference methods.

Work Placement(s)

No

Syllabus

1. Modeling for engineering design and analysis. Error analysis. introduction to MATLAB

2. Solving Nonlinear Equations and linear and nonlinear Systems of Equations.

3. Approximation and Numerical Differentiation and Integration.

4. Ordinary differential equations (ODEs). Initial value problem and Boundary value problem. Applications in Environmental Engineering (Mathematical models of population dynamics.  Streeter-Phelps model. Solutions of Lotka-Volterra equations).

5. Partial Differential Equations (PDEs). Algorithms of finite difference methods for numerical solution of differential equations including elliptic, parabolic and hyperbolic PDE's. Applications in Environmental Engineering (The generic scalar transport equation. Pure convection and pure diffusion problems, convection-diffusion and wave equation. Water quality and groundwater modeling applications).

Head Lecturer(s)

José Manuel de Eça Guimarães de Abreu

Assessment Methods

Assessment
Exam: 40.0%
Resolution Problems: 60.0%

Bibliography

Abreu, J.M, Antunes do Carmo, J. S.  (2015) - Métodos Numéricos em Engenharia, DEC-FCTUC

Chapra, S.C., Canale, R.P. (2015) - Numerical methods for engineers. McGraw-Hill Int. Eds., 7th Edition

Curtis, F.G., Wheatley, P.O. (1994) - Applied numerical analysis. Addison Wesley, 5th Edition

Gilat, A., Subramaniam, V. (2014) - Numerical Methods for Engineers and Scientists. An Introduction with Applications using MATLAB. Wiley, 3rd Edition

Jaluria (2011)Computer Methods for Engineering with MATLAB® Applications. CRC Press. 2^nd Edition

Kiusalaas, J. (2016) - Numerical Methods in Engineering with MATLAB; Cambridge University Press. 3rd Edition.