• Inactive for Year: 2024/25

• Module Leader(s): Dr Chris Graham
• Lecturer: Dr Andrew Baggaley

• Owning School: Mathematics, Statistics and Physics
• Teaching Location: Newcastle City Campus

Semesters

Your programme is made up of credits, the total differs on programme to programme.

Aims

To reinforce the computing in Python studied within MAS1801, and to move towards expectations of more independent programming. To introduce a wider range of mathematical techniques within Python, including methods that will be useful towards future project work. To introduce the fundamental concepts and governing equations of fluid mechanics, using mathematical techniques to analyse simple flow problems for an inviscid (frictionless) fluid.

Module Summary
Computing methods are of great use in a wide range of applications applied mathematics. This module builds on the methods introduced in MAS1801, introducing additional techniques, some of increasing mathematical and computational sophistication. In implementing these methods, students will attain increasing competence with mathematical computing, and an increasing ability to use such methods independently, towards project-orientated goals.

Fluid dynamics plays a central role in many natural phenomena. As we breathe, gas flows in and out of our lungs, whilst our heart pumps blood around the body. Without a proper understanding of large-scale fluid flows in the Earth’s atmosphere and oceans, it would be impossible for meteorologists to produce reliable weather forecasts. On yet larger scales, the complex motions in the Earth’s molten iron core are responsible for sustaining the terrestrial magnetic field. The principles of fluid dynamics can also be used to explain aerodynamic lift, whilst engineers need to be able to model fluid flows around solid bodies (like tall buildings) and along pipes.

This module will introduce the concept of a fluid, and the ways in which the motions of such a system can be described. The main focus of this module will be on the dynamics of inviscid (frictionless) fluids. Even with such an assumption, it is not possible to write down a general solution of the governing equations, but it is possible to make certain simplifying assumptions to deduce the properties of certain flows.

Outline Of Syllabus

Python:
⦁       Plotting of vector fields and trajectories.
⦁       Curve fitting (e.g. least squares fitting of known function to data).
⦁       Root finding (Newton-Raphson and Python solvers).
⦁       Numerical derivatives through finite difference, and related techniques of numerical integration.
⦁       Numerical solution of ordinary differential equations.

Fluid dynamics:
•      Continuum approximation
•      Kinematics: Streamlines, pathlines, steady and time-dependent flows, convective derivative, vorticity and circulation.
•       Governing equations and elementary dynamics: Conservation of mass, the continuity equation and incompressibility, Euler’s equation, Bernoulli’s streamline theorem.
•       Irrotational flows and potential theory: Laplace’s equation, principle of superposition, simple examples including sources, sinks and line vortices, flow around a cylinder and sphere.
•       Linear water waves: Surface waves (deep and shallow), dispersive waves, group velocity.

Teaching Methods

Teaching Activities

Teaching Rationale And Relationship

Non-synchronous online materials are used for the delivery of theory and explanation of methods, illustrated with examples, and for giving general feedback on assessed work. Present-in-person and synchronous online sessions are used to help develop the students’ abilities at applying the theory to solving problems and to identify and resolve specific queries raised by students, and to allow students to receive individual feedback on marked work. Students who cannot attend a present-in-person session will be provided with an alternative activity allowing them to access the learning outcomes of that session. In addition, office hours/discussion board activity will provide an opportunity for more direct contact between individual students and the lecturer: a typical student might spend a total of one or two hours over the course of the module, either individually or as part of a group.

Alternatives will be offered to students unable to be present-in-person due to the prevailing C-19 circumstances.
Student’s should consult their individual timetable for up-to-date delivery information.

Assessment Methods

The format of resits will be determined by the Board of Examiners

Exams

Other Assessment

Assessment Rationale And Relationship

A substantial formal examination is appropriate for the assessment of the material in this module. The course assessments will allow the students to develop their problem solving techniques, to practise the methods learnt in the module, to assess their progress and to receive feedback; these assessments have a secondary formative purpose as well as their primary summative purpose.

Reading Lists

• MAS2805's Reading List

Timetable

• Timetable Website: www.ncl.ac.uk/timetable/
• MAS2805's Timetable