Continuum Mechanics and Industrial Modelling (3A5)

The lecturer is Nev Fowkes Rm 1.15 (fowkes@maths.uwa.edu.au).

Unit Aims

This course provides basic background material required for students who intend to proceed on to a career in modelling in the Physical Sciences or Engineering. The attitudes and skills required for modelling are emphasized. Students are expected to use Maple or Mathematica to process models. For introductory note see below. Areas covered include Diffusion (primarily in a heat conduction context), Wave Propagation (primarily in the context of traffic dynamics), and the foundations of Continuum Mechanics will be discussed mainly in a fluid mechanics setting. A wide variety of real world problems that have arisen recently from Industry will be discussed.

Assessment

One three hour exam worth 70% of the final grade.
Two take home assignments each worth 15% of the final grade.

Exercise Sheets

Exercise sheets will be handed out regularly and solutions will be distributed.

Unit Content

Diffusion Processes

The Heat Equation. Scaling ideas. Elementary solution properties. The fundamental plane source solution. Other fundamental solutions. Boundary Integral methods. Numerical schemes (difference schemes, finite elements). Greenhouse Modelling. Cooking Problems. State Change problems.

Non-Linear Waves

Traffic Dynamics. Information speed. Shock waves.

Continuum Mechanics

The stress tensor. Constitutive relations for solids and fluids. Lagrangian and Eulerial descriptions of motion. Equations of motion. Inspectional analysis. Dimensionless groups.

Lecture Notes

Typed notes covering most of the material of the course are provided, see below.

Recommended Reading

Fowkes and Mahony: An Introduction to Mathematical Modelling Wiley (94)

Segel and Handelman: Mathematics applied to Continuum Mechanics, Macmillan (77)

Acheson D. J. : Elementary Fluid Dynamics, Clarendon Press (89)

Important Announcements:

Here I will place announcements concerning assignments for credit etc.

Solutions to Assignment 2 are now available, see below. and also Assignment 2 is now available. Please read the following document regarding plagiarism. For the Assignments students may discussgeneral principles with fellow students and tutors and seek help from tutors, but must submit an individual piece of work, which must be submitted on time for credit. Concerning the Faculty policy for Appeals see appeals.

The examination will be of 3 hours duration and will consist of 5 questions, all of which should be attempted.Only standard calculators will be permitted. No notes books etc.The exams in 2002, 2003 are reasonably representative of what to expect. You'll find the 2002 paper with solutions below.

Exercise Sheets and Assignments