Module manager: Dr. Amirul Khan
Email: a.khan@leeds.ac.uk
Taught: Semester 2 (Jan to Jun) View Timetable
Year running 2026/27
Admission to UG programmes in the School of Civil Engineering
This module is not approved as a discovery module
This module equips students with the skills to apply numerical methods to real-world civil engineering problems. Students learn to model physical systems such as heat transfer, fluid flow, and structural dynamics. These problems are governed by differential equations and students learn how finite element methods are applied to solving them using commercial software. Through a mix of lectures, tutorials, and a hands-on mini-project, students develop the ability to discretise problems, implement computational solutions, and interpret results critically. The module blends mathematical theory with a very practical application, preparing students to tackle complex engineering challenges using modern computational techniques.
The objectives of this module are:
- To understand the principles of discretising continuum engineering problems governed by partial differential equations.
- To learn the mathematical fundamentals needed to numerically solve differential equations, namely: finite difference (FDM) and finite volume (FVM) methods, and the finite element method (FEM).
- To recognise when and how these to apply these methods to the modelling physical phenomena and to find solutions to complex problems.
- To learn how to choose, formulate and implement the appropriate numerical methods for solving engineering problems described by partial differential equations.
- To understand how to interpret, analyse and evaluate results from numerical computations.
- To develop confidence in the use of commercial tools, solvers and coding environments to solve engineering problems governed by partial differential equations.
- To develop an awareness of the challenges, limitations and common issues relevant to the application of these methods in real contexts.
On successful completion of the module students will be able to:
1. Understand and apply the mathematical principles that underpin the numerical modelling and analysis techniques used in modern engineering practice.
2. Distinguish between types of partial differential equations and recognise their applications.
3. Formulate simple finite difference expressions using Taylor series and apply the principles of finite difference and finite volume methods to a range of engineering problems.
4. Use a variety of software tools and solvers to understand, model and solve problems like fluid flow or heat transfer.
5. Explain finite differences and finite volume techniques and the main steps of developing a model using these approaches.
6. Analyse linear and nonlinear systems of partial differential equations and solve time-dependent problems using the finite differences and finite volume methodologies using computational tools.
On successful completion of the module students will be able to:
Academic Skills:
- Apply mathematical principles to numerical techniques used in engineering practice.
- Formulate and solve ordinary and partial differential equations.
- Analyse and interpret results from numerical simulations and computational models.
Digital Skills:
- Use commercial software to model and solve engineering problems.
- Develop proficiency in computational tools for simulation and analysis of physical systems.
- Implement numerical algorithms and interpret digital outputs effectively.
Work-Ready Skills:
- Manage a mini-project independently, including planning, execution, and reporting.
- Communicate technical findings clearly through written reports and presentations.
- Collaborate in group learning activities and engage in problem-based learning environments.
- Problem Solving and Analytical Skills:
- Identify appropriate numerical methods for different problems.
- Evaluate the accuracy and limitations of computational models.
- Apply logical reasoning and critical thinking to engineering scenarios.
Professional Literacy:
- Translate theoretical knowledge into practical applications relevant to civil engineering.
- Demonstrate initiative and independence in tackling complex modelling tasks.
- Numerical methods for ordinary differential equations (ODEs): numerically defined functions; Taylor’s series and truncation error; numerical differentiation: boundary value problems, initial value problems; Euler’s method and higher order Runge-Kutta methods.
- Principles of meshing and its implications on discretisation accuracy.
- Initial- and boundary-value problems for ordinary differential equations using shooting techniques and difference methods.
- Numerical solution of partial differential equations using difference methods; introduction to the finite element method.
- Explicit and implicit schemes focused on one-dimensional transient problems. Fourier stability analysis.
- Stationary problems in two dimensions: heat transfer, dynamics, elasticity and fluid mechanics.
Methods of assessment
The assessment details for this module will be provided at the start of the academic year
| Delivery type | Number | Length hours | Student hours |
|---|---|---|---|
| Supervision | 5 | 1 | 5 |
| Lectures | 5 | 2 | 10 |
| Practicals | 2 | 3 | 6 |
| Independent online learning hours | 20 | ||
| Private study hours | 59 | ||
| Total Contact hours | 21 | ||
| Total hours (100hr per 10 credits) | 100 | ||
Formative Problem activities (Matlab task)
In class interactivity
Meetings during mini-project
Check the module area in Minerva for your reading list
Last updated: 30/04/2026
Errors, omissions, failed links etc should be notified to the Catalogue Team