Module manager: Dr Alison Jones
Email: a.c.jones@leeds.ac.uk
Taught: Semesters 1 & 2 (Sep to Jun) View Timetable
Year running 2026/27
Undergraduate training in solid mechanics, fluid mechanics and materials, to EQF Level 5. A-level standard matrix algebra and calculus.
| MECH1215 | Thermofluids 1 |
| MECH1230 | Solid Mechanics |
| MECH1520 | Engineering Mathematics |
| MECH2610 | Engineering Mechanics |
| MECH2670 | Thermofluids 2 |
MECH3900, Finite Element Methods of Analysis
This module is not approved as a discovery module
This module is approved as a skills discovery module
This module provides the theoretical and practical knowledge to allow a student to competently perform Computational Fluid Dynamics (CFD) analysis of fluids problems and Finite Element Analysis (FEA) of structural problems, using commercial software packages used in industry. This is taught through a series of self-study components with follow up lecture sessions covering the underpinning theory and quality control processes. Additionally, practical sessions establish software skills for the development and solution of computational models, provide links to theory, rehearse problem solving including fault diagnostics and develop critical analysis.
On successful completion of the module students will;
1. Understand the governing equations for the numerical simulation of solid mechanics and fluid dynamics;
2. To appreciate the limitations of numerical methods/algorithms required for solving a range of engineering problems;
3. Appreciate the challenges and limitations of the application CFD and FEA, including the importance of verification and validation;
4. Evaluate and select the most appropriate discretisation and solution strategy for various applications;
5. Undertake the simulation and analysis of practical problems using commercial CFD and FEA codes and critically assess the output solution.
Theoretical understanding (#1 and the underpinning of #2-4) will be developed through a combination of structured self-study and lecture sessions, providing a combination of definitions, derivations and examples. Software skills (#5) will be initially established through structured exercises and developed (#2-5) through live practical sessions and an applied assignment.
Subject specific learning outcomes:
On successful completion of the module students will be able to:
1. Explain and illustrate the basic principles of structural analysis using finite element methods, including shape functions and stiffness matrices (in 1D and 2D);
2. Understand the interplay between governing equations for fluid dynamics and flow assumptions to set up computer simulations correctly;
3. Understand the basic principles of fluid dynamics to be able to identify various flow features including boundary layers and separated/attached flows;
4. Appreciate the limitations of numerical methods/algorithms required for solving both solid mechanics and fluid dynamics problems;
5. Understand the role of boundary conditions, mesh design and solver settings to generate meaningful engineering solutions;
6. Ability to recognise the challenges and limitations of computational approaches to both structural and fluids problems;
7. Understand the principles of quality control through the application of verification and validation procedures;
8. Evaluate and select the most appropriate methods of analysis for various real-life applications;
9. Critically assess the simulation outputs and understand how to interpret them to gain meaningful engineering insights.
These module learning outcomes contribute to the following AHEP4 learning outcomes:
- Apply knowledge of mathematics, statistics, natural science and engineering principles to the solution of complex problems. Some of the knowledge will be at the forefront of the particular subject of study. [C1]
- Analyse complex problems to reach substantiated conclusions using first principles of mathematics, statistics, natural science and engineering principles. [C2]
- Select and apply appropriate computational and analytical techniques to model
complex problems, recognising the limitations of the techniques employed. [C3]
On successful completion of the module students will have demonstrated the following skills:
a. Development of self-confidence, initiative and perseverance in setting up and solving computational problems;
b. Active learning through doing and reflection of best practice in computational lab environments;
c. Practice in the use of information technology including digital proficiency and productivity through the application of computational simulation techniques;
d. Application of problem-solving strategies including adaptability and integration of multiple sources of information;
e. Interpretation of visual information to aid decision making and to enhance critical thinking in engineering systems;
f. Application of innovation and creativity to improve systems thinking.
g. Proficiency of academic writing and visual communication to enhance presentation skills;
h. Effective time management, planning, organisation and working under time pressure.
Common syllabus themes
- Mathematical idealisation of real structural and fluids problems including assumptions and simplifications.
- Boundary conditions, initialisation and iterative procedures.
- Mesh design, verification and numerical error estimation.
- Implementation of numerical methods to generate informative quantitative and qualitative data.
- Model validation approaches and dealing with sources of error and uncertainty.
Computational Fluid Dynamics
1. Overview of Computational Fluid Dynamics
2. Navier-Stokes equations and flow assumptions for a range of engineering applications
3. Principles of iterative methods and numerical schemes including discretisation, convergence and stability
4. Mesh generation including best practice guidelines
5. Boundary condition types, uses and implementation
6. Solver types, grid staggering and the finite volume method
7. Pressure-velocity coupling algorithms, gradient schemes and initialisation methods
8. Turbulence modelling including the energy cascade, hierarchy of models (RANS, URANS, DES, LES & DNS) and wall functions
9. Multi-physics simulations: multiphase flow, heat transfer & radiation modelling, species transport, discrete phase modelling and fluid-structure interaction (FSI).
10. Quality control in CFD through verification and validation procedures
11. Post-processing, data presentation and interpretation of flow physics
12. Effective simulation strategies including fault diagnostics and overall best practice
Finite element analysis
1. Introduction to finite element analysis
2. Principle of minimum structural potential Derivation of potential equations and finite element formulation
3. Derivation of shape function and stiffness matrix (truss, beam elements)
4. Derivation of force vectors (point forces and distributed forces)
5. Transformation in 2 and 3D (truss elements)
6. Assembly of global stiffness matrix and load vectors (truss, beam elements)
7. Application of boundary conditions
8. Solution of equations.
9. Relationship between nodal displacements and strain/stress.
10. Two-dimensional elasticity finite elements; plane stress, plane strain and axisymmetric stress states
11. Derivation and use of key matrices for 2D elasticity finite elements
12. Derivation of force vectors for 2D finite element
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 |
|---|---|---|---|
| Lecture | 22 | 1 | 22 |
| Practical | 7 | 2 | 14 |
| Independent online learning hours | 44 | ||
| Private study hours | 120 | ||
| Total Contact hours | 36 | ||
| Total hours (100hr per 10 credits) | 200 | ||
In computer lab sessions, students will receive regular formative feedback through discussion with module staff and demonstrators. There will be opportunities for instant formative feedback via MCQs and through completion of tasks in lab sessions. Drop in sessions supporting the coursework assignment are opportunities to discuss ideas and check understanding of the task.
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