# NUMERICAL METHODS & CFD - 2020/1

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

### Module Leader

MARXEN Olaf (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

## Overall student workload

Independent Learning Hours: 108

Lecture Hours: 22

Tutorial Hours: 20

## Module Availability

Semester 1

## Prerequisites / Co-requisites

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 |
---|---|---|

Examination | EXAMINATION (2HRS) | 70 |

Coursework | CFD ASSIGNMENT | 15 |

Coursework | NUMERICAL METHODS ASSIGNMENT | 15 |

## Alternative Assessment

NA

## 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 computer-based tool 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 implement this solution method. 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 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:

- 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

https://readinglists.surrey.ac.uk

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 2020/1 academic year.