# NUMERICAL METHODS & CFD - 2021/2

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 numerical methods often used in engineering software. The students use a computer-based tool to solve a simple engineering flow problem of interest to their discipline.

### Module provider

Mechanical Engineering Sciences

MARXEN Olaf (Mech Eng Sci)

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

Independent Learning Hours: 97

Lecture Hours: 11

Tutorial Hours: 20

Captured Content: 22

Semester 1

None

## 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; numerical integration and quadrature; the concept of modified wave number.

• Explicit and implicit methods for the integration of ordinary differential equations.

• Analysis of numerical schemes: consistency, stability and convergence; Lax' equivalence theorem; von Neumann and Fourier analysis.

• Methods and combined analysis of spatio-temporal discretization for partial differential equations; amplitude and phase errors including numerical dispersion and diffusion; the convection-based CFL number and corresponding diffusion number.

CFD:

• Introduction to the modelling process for fluids engineering

• Geometry modelling

• Grid generation techniques

• Discussion of solution methods, convergence and accuracy of flow solvers

• Computation of the Navier-Stokes equations: finite-volume discretization and pressure-velocity coupling

• Verification and validation

• The role of boundary conditions

• Post-processing

• Brief overview of advanced CFD techniques

## Assessment pattern

Assessment type Unit of assessment Weighting
Online Scheduled Summative Class Test CFD CLASS TEST 25
Coursework CFD LAB. REPORT 25
Examination Online ONLINE EXAM 24HRS (OPEN BOOK) 50

NA

## Assessment Strategy

The assessment strategy is designed to provide students with the opportunity to demonstrate understanding of the basic numerical and CFD 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 computer-based tool and their awareness of the possible sources of error in the solution. The numerical methods final examination assesses the students' theoretical knowledge of numerical methods, as well as their ability to implement these methods to solve simple partial differential equations as they often occur in engineering.

Thus, the summative assessment for this module consists of:

Examination      NUMERICAL METHODS ONLINE EXAMINATION   50%
Coursework       CFD LAB. REPORT            25%
Class Test           CFD CLASS TEST 25%

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 and to understand the possible sources of error in a computational fluid dynamics (CFD) simulation
• enable the students to use a computer-based tool to perform a simulation of a simple flow of engineering interest, including pre- and post-processing

## Learning outcomes

 Attributes Developed 001 Select and implement an appropriate numerical method for common practical engineering problems (SM2b, SM2m, EA2, EA6m, EA3b, EA3m) KCP 002 Understand the sources of error in a numerical solution and evaluate the validity of numerical solutions ) (EA2, SM2b, SM2m) C 003 Solve a simple engineering flow problem using a computer-based tool (SM2b, SM2m, EA2, EA6m, EA3b, EA3m) KCP

Attributes Developed

C - Cognitive/analytical

K - Subject knowledge

T - Transferable skills

P - Professional/Practical skills

## 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 practical coursework assignments.

The learning and teaching methods include:

• 1 hours lecture per week (11 weeks = 11 hours)

• 2 hours tutorial per week (10 weeks = 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.

Upon accessing the reading list, please search for the module using the module code: ENG3165

## Programmes this module appears in

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

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 2021/2 academic year.