# 2017/18 Taught Postgraduate Module Catalogue

## MATH5453M Foundations of Fluid Dynamics

### 30 creditsClass Size: 30

Module manager: Dr Oliver Harlen, Professor Onno Bokhove
Email: O.G.Harlen@leeds.ac.uk, O.Bokhove@leeds.ac.uk

Taught: Semester 1 View Timetable

Year running 2017/18

### Pre-requisite qualifications

Admissions to the CDT in Fluid Dynamics or MSc in Atmosphere-Ocean Dynamics

This module is not approved as an Elective

### Module summary

This module will prepare students intending to do a fluids related PhD.It is relevant to a wide range of application areas in which fluids dynamics plays an important role: in engineering, applied mathematics, atmosphere or ocean dynamics, or astrophysical or geophysical fluid dynamics. The module will involve fundamental theory, numerical and experimental methods so that students will get an overview of all the main methods by which fluid dynamics problems can be tackled.

### Objectives

The module will give students from potentially different backgrounds the core skills they will need in the fundamental theory of fluid dynamics, numerical methods and experimental methods to successfully complete a PhD in a research area with a significant fluids component.

Learning outcomes
Students will understand the fundamental theoretical concepts of fluid dynamics and how they can be applied to solve engineering and scientific problems.

They will be aware of the principal numerical methods used to solve fluid dynamics problems. They will have practical experience of developing successful codes to find numerical solutions of basic fluid flows. They will understand the basic concepts of the numerical modelling of laminar and turbulent flows.

Students will be familiar with the basic techniques of experimental fluid dynamics. They will have had practical experience of setting up and measurement for laboratory fluid dynamics experiments.

Students will have gained experience of the interactions between CFD, analytic models and experiments.

### Syllabus

Underlying theory will include:

1. Continuum description of fluids. Streamfunction and vorticity. Stress and strain rate tensors, distinction between Newtonian and non-Newtonian fluids;

2. Navier-Stokes equation and exact solutions. Low and high Reynolds number approximations, and where they can be applied;

3. Scaling and dimensionless numbers in fluid dynamics;

4. Conservation laws of fluid dynamics;

5. Heat equation, convection and heat transfer;

6. Wave motion, phase velocity and group velocity. Applications to water waves, sound waves and internal gravity waves;

7. Boundary layers. Separation;

8. Introduction to rotating and MHD flows;

Numerical methods will include:

9. Finite difference, finite volume and finite element methods;

10. Error and stability of numerical schemes. Timestepping schemes;

11. Conservative schemes;

12. Spectral methods and spectral elements;

13. Smooth particle hydrodynamics.

Experimental Methods will include:

14. Design of experiments, scale analysis. Links between experiments, theory and CFD;

15. Anemometry measurements, velocimetry techniques. Error analysis;

16. Atmospheric measurements.

### Teaching methods

 Delivery type Number Length hours Student hours Laboratory 4 2.00 8.00 Lecture 37 1.00 37.00 Practical 5 2.00 10.00 Seminar 22 1.00 22.00 Tutorial 4 1.00 4.00 Private study hours 219.00 Total Contact hours 81.00 Total hours (100hr per 10 credits) 300.00

### Private study

There will be 4 assessed example sheets to complete, and 4 computer practical exercises to complete. The laboratory based work will be written up and assessed. There will be a substantial reading list, with recommendations as to which sections need to be mastered. The theory and the numerical sections will have four lectures a week. The seminar sessions will be led by members of the Fluids CDT team, within the Faculties of MAPS, Environment and Engineering.

It is intended that students will help each other prepare for these tasks, so 20 hours is allocated to group learning.

### Opportunities for Formative Feedback

The in-course assessment of the example sheets, computer practicals and lab work will allow staff to monitor students' progress. This will be used to advise students were there is any cause for concern about particular areas where students may be having difficulties.

### Methods of assessment

Coursework
 Assessment type Notes % of formal assessment Practical Experimental Lab Assessment 20.00 Practical Assessment of the 4 Computational practicals 20.00 Problem Sheet 4 example sheets will be marked 20.00 Total percentage (Assessment Coursework) 60.00

Normally resits will be assessed by the same methodology as the first attempt, unless otherwise stated

Exams
 Exam type Exam duration % of formal assessment Standard exam (closed essays, MCQs etc) 2 hr 30 mins 40.00 Total percentage (Assessment Exams) 40.00

Normally resits will be assessed by the same methodology as the first attempt, unless otherwise stated