Module code: ENG3165

Module Overview

Third year module in numerical methods for engineering problems.

The module introduces the typical methods used in engineering practice to obtain numerical solutions to problems described by differential equations.  MATLAB is used to allow the students to test the numerical methods on appropriate problems. The emphasis is on understanding the applicability and limitations of the methods used in engineering software. The students are introduced to a commercial CFD package and solve a simple engineering flow problem of interest to their discipline.


Module provider

Mechanical Engineering Sciences

Module Leader

CARPENTIERI Matteo (Mech Eng Sci)

Number of Credits: 15

ECTS Credits: 7.5

Framework: FHEQ Level 6

JACs code: G140

Module cap (Maximum number of students): N/A

Module Availability

Semester 1

Prerequisites / Co-requisites


Module content

Indicative content includes:

Numerical methods:

Introduction to numerical solution of fluid dynamics problems: conservation equations, Navier-Stokes, workflow for numerical solution methods.
Partial differential equations: order, linearity and classification (elliptic, parabolic and hyperbolic equations)
Finite difference methods (FDM): discretisation, grid and approximations; finite difference approximation for the first and second derivatives and their accuracy; explicit and implicit Euler methods; Cranc-Nicolson method.
Analysis of numerical schemes: consistency, stability and convergence; Lax' equivalence theorem; consistency analysis; the modified differential equation; stability and numerical diffusion; the CFL number.
Computation of the Navier-Stokes equations: pressure-velocity coupling; semi-discretisation and full discretisation.


Introduction to the modelling process for fluids engineering
Geometry modelling
Grid generation techniques
Introduction to commercial CFD software
Discussion of solution methods, convergence and accuracy of flow solvers
Verification and validation
The role of boundary conditions
Brief overview of advanced CFD techniques 

Assessment pattern

Assessment type Unit of assessment Weighting
Examination EXAMINATION (2HRS) 70
Coursework CFD ASSIGNMENT 15

Alternative Assessment


Assessment Strategy

The assessment strategy is designed to provide students with the opportunity to demonstrate understanding of the basic numerical methods as well as the ability to select appropriate methods and obtain numerical solutions to engineering problems. The CFD coursework assignment tests the students’ ability to obtain a solution to a flow problem using a commercial CFD solver and their awareness of the possible sources of error in the solution. The numerical methods coursework assignment tests the students’ ability to select an appropriate numerical method for an engineering problem and their ability to code this solution method in MATLAB. The final examination assesses the students' theoretical knowledge of numerical methods and CFD, as well as their ability to solve simple problems.

Thus, the summative assessment for this module consists of:

CFD assignment – [Learning outcomes 2,3] – 10 hours (15%)
Numerical methods assignment [Learning outcomes 1,2] – 10 hours (15%)
Examination [Learning outcomes 1,2] – 2 hours (70%)

Formative assessment and feedback

Formative verbal assessment is given in tutorials and lectures (through electronic voting sessions)

Written feedback is given on coursework assessments

Module aims

  • introduce the students to the numerical methods used for solution of engineering problems
  • expand the students' programming skills in MATLAB to allow them to implement numerical methods for engineering problems
  • provide the students with the criteria for the selection of appropriate methods and to critcally assess the validity of their solutions
  • enable the students to understand the steps needed to compute a solution to a problem in fluid dynamics using a CFD code and to understand the possible sources of error in a CFD simulation
  • enable the students to use a CFD code to run a simulation of a simple flow of engineering interest, including pre- and post-processing

Learning outcomes

Attributes Developed
1 Select and implement an appropriate numerical method for common practical engineering problems (SM2b, SM2m, EA2, EA6m, EA3b, EA3m) KCP
2 Understand the sources of error in a numerical solution and evaluate the validity of numerical solutions ) (EA2, SM2b, SM2m) C
3 Solve a simple engineering flow problem using a CFD package (SM2b, SM2m, EA2, EA6m, EA3b, EA3m) KCP

Attributes Developed

C - Cognitive/analytical

K - Subject knowledge

T - Transferable skills

P - Professional/Practical skills

Overall student workload

Independent Study Hours: 108

Lecture Hours: 22

Tutorial Hours: 20

Methods of Teaching / Learning

The learning and teaching strategy is designed to introduce numerical methods and CFD through theory with worked examples carried out by the students. This is delivered through lectures and tutorial classes with the students conducting two practical coursework assignments.

The learning and teaching methods include:

2 hours lectures per week (11 weeks = 22 hours)
2 hours tutorial per week (10 weeks = 20 hours)
Coursework assignments (20 hours)

Indicated Lecture Hours (which may also include seminars, tutorials, workshops and other contact time) are approximate and may include in-class tests where one or more of these are an assessment on the module. In-class tests are scheduled/organised separately to taught content and will be published on to student personal timetables, where they apply to taken modules, as soon as they are finalised by central administration. This will usually be after the initial publication of the teaching timetable for the relevant semester.

Reading list

Reading list for NUMERICAL METHODS & CFD :

Programmes this module appears in

Programme Semester Classification Qualifying conditions
Mechanical Engineering MEng 1 Compulsory A weighted aggregate mark of 40% is required to pass the module
Automotive Engineering MEng 1 Compulsory A weighted aggregate mark of 40% is required to pass the module
Aerospace Engineering BEng (Hons) 1 Optional A weighted aggregate mark of 40% is required to pass the module
Aerospace Engineering MEng 1 Compulsory A weighted aggregate mark of 40% is required to pass the module
Automotive Engineering BEng (Hons) 1 Optional A weighted aggregate mark of 40% is required to pass the module
Mechanical Engineering BEng (Hons) 1 Optional A weighted aggregate mark of 40% is required to pass the module

Please note that the information detailed within this record is accurate at the time of publishing and may be subject to change. This record contains information for the most up to date version of the programme / module for the 2018/9 academic year.