Undergraduate Programme and Module Handbook 2018-2019 (archived)
Module MATH4081: CONTINUUM MECHANICS IV
Department: Mathematical Sciences
MATH4081:
CONTINUUM MECHANICS IV
Type |
Open |
Level |
4 |
Credits |
20 |
Availability |
Not available in 2018/19 |
Module Cap |
|
Location |
Durham
|
Prerequisites
- (Problem Solving and Dynamics (MATH1041) OR Foundations of Physics I
(PHYS1122)) AND mathematics modules to the value of 100 credits in Years
2 and 3, with at least 40 credits at Level 3, and including Analysis in
Many Variables II (MATH2031).
Corequisites
Excluded Combination of Modules
- Continuum Mechanics III (MATH3101).
Aims
- To introduce a mathematical description of fluid flow and other
continuous media to familiarise students with the successful
applications of mathematics in this area of modelling.
- to prepare students for future study of advanced topics.
Content
- Kinematic description of fluid flows: streamlines and
trajectories, mass conservation and continuity equation
- Review of tensors, stress and rate of
strain.
- Dynamical models of fluid flows: Euler and Navier-Stokes
equation.
- Some methods to solve Euler and Navier-Stokes
equations.
- Waves: sound and water waves, linear and
nonlinear
- Topics from: thermodynamics, scaling and dimensional
analysis, hydrodynamic stability, NSE and turbulence, non-Newtonian
fluid flows
- Reading material on a topic related to: hydrodynamic
stability, turbulence.
Learning Outcomes
- By the end of the module students will: be able to solve
complex, unpredictable and specialised problems in Continuum
Mechanics.
- have an understanding of specialised and complex theoretical
mathematics in the field of Continuum Mechanics.
- have mastered a coherent body of knowledge of these subjects
demonstrated through one or more of the following topic areas:
Kinematics of fluid flows.
- Equations of motion and their derivation for
fluids.
- have an advanced understanding in one of the following areas:
hydrodynamic stability, turbulence.
- In addition students will have highly specialised and
advanced mathematical skills in the following areas:
Modelling.
- They will be able to formulate and use mathematical models in
various situations.
- Students will be able to study independently to further their
knowledge of an advanced topic.
Modes of Teaching, Learning and Assessment and how these contribute to
the learning outcomes of the module
- Lectures demonstrate what is required to be learned and the
application of the theory to practical examples.
- Assignments for self-study develop problem-solving skills and
enable students to test and develop their knowledge and
understanding.
- Formatively assessed assignments provide practice in the
application of logic and high level of rigour as well as feedback for
the students and the lecturer on students' progress.
- The end-of-year examination assesses the knowledge acquired
and the ability to solve complex and specialised problems.
Teaching Methods and Learning Hours
Activity |
Number |
Frequency |
Duration |
Total/Hours |
|
Lectures |
42 |
2 per week for 20 weeks and 2 in term 3 |
1 Hour |
42 |
|
Problems Classes |
8 |
Four in each of terms 1 and 2 |
1 Hour |
8 |
|
Preparation and Reading |
|
|
|
150 |
|
Total |
|
|
|
200 |
|
Summative Assessment
Component: Examination |
Component Weighting: 100% |
Element |
Length / duration |
Element Weighting |
Resit Opportunity |
Written examination |
3 Hours |
100% |
|
Eight written assignments to be assessed and
returned. Other assignments are set for self-study and complete solutions
are made available to students.
■ Attendance at all activities marked with this symbol will be monitored. Students who fail to attend these activities, or to complete the summative or formative assessment specified above, will be subject to the procedures defined in the University's General Regulation V, and may be required to leave the University