Computational Engineering { Finite Di erence Techniques
Transcript of Computational Engineering { Finite Di erence Techniques
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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