Computational Engineering { Finite Di�erence

Techniques

SOE3213/4: FD Lecture 1

1.1 Course outline

3 sections :

1. Introduction, Finite Di�erence methods (GRT)

2. Finite Volume for CFD (Computational Fluid Dynamics) (GRT)

3. Finite Elements (PGY)

Assessment :

� 30% coursework exercises (FD, FE, FV)

� 30% Miniproject I (Submit Wk 8)

� 40% Miniproject II (Submit Wk 11)

1.2 Lectures etc

Week Lecture 1 Lecture 2 Comp Lab1 FD FD2 FD FD3 FE CFD FE/CFD Lab4 FE CFD FE/CFD Lab5 FE CFD FE/CFD Lab6 FE CFD

2 lectures/week : Tue 12pm, Thurs 9am. CFD/FE Tutorial labs Wk3-Wk5

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1.3 Code web sites

Fluent (CFD code)

http://www. uent.com/

http://www. uent.com/solutions/index.htm

Abaqus (FEA code)

http://www.abaqus.com/

http://www.abaqus.com/solutions/solutions.html

1.4 Examples

4th year miniproject { Nascar racing car

Femoral artery

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American Solar Challenge { University of Waterloo, Canada

See : http://www.engineers.auckland.ac.nz/ snor007/cfd.html for details

FEA Stress

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1.5 Partial Di�erential Equations

PDE { equations relating partial derivatives of variables. Typically want tosolve to �nd how dependent variable(s) (temperature, pressure, stress etc) varyas functions of independent variables (position, time).

E.g. Heat transfer { governing equation

@T

@t= �

@2T

@x2

{ heat conduction equation.

� T { dependent variable

� x, t { independent variables

Note : T de�ned at all points in space and time { continuum mechanicsproblem.

Solution to T will depend on mathematics of governing equation { and onboundary conditions applied.

1.6 Summary

� Numerous continuum mechanics problems in engineering

� Generally insoluble analytically

� Use numerical methods instead

� Prewritten packages widely used in industry

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{ but important to understand theoretical basis

{ and to approach results critically

� Learn FD techniques as basis, FE and CFD for applications

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