An introduction to relaxation and how it can be used to help improve convergence in CFD.
Time stamps:
0:00 Introduction
0:48 Recap
3:52 Implicit Relaxation
7:12 Compact Form
9:16 Explicit vs Implicit
10:25 Mathematical Derivation
12:46 Formula Comparison
15:43 Matrix Form
17: 24 Diagonal Dominance
22:58 History
24:30 OpenFOAM (fvSolution)
28:30 Summary
29:28 Outro
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Some useful references
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1. Ferziger & Peric, 'Computational Methods for Fluid Dynamics', 3rd Edition, Springer-Verlag, Berlin, Heidelberg, New York, 2002.
www.amazon.co.uk/Computationa... [Page 118, 149]
2. S. Patankar, 'Numerical Heat Transfer and Fluid Flow', 1st Edition, McGraw-Hill, 1980. [Page 67]
2. ANSYS Fluent 12.0 User manual (18.4.4 Steady-State Iterative Algorithm)
www.afs.enea.it/project/neptu...
3. OpenFOAM: User Guide v2012. Under relaxation
www.openfoam.com/documentatio...
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Disclaimer
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The methods, algorithms, equations, formulae, diagrams and explanations in this talk are for educational and demonstrative purposes only. They should never be used to analyse, design, accredit or validate real scientific / engineering / mathematical structures and flow systems. For such applications, appropriate trained, qualified and accredited (SQEP) engineers / scientists should be consulted along with the appropriate documentation, procedures and engineering standards. Furthermore, the information contained within this talk has not been verified, peer reviewed or checked in any way and is likely to contain several errors. It is therefore not appropriate to use this talk itself (or any of the algorithms, equations, formulae, diagrams and explanations contained within this talk) as an academic or technical reference. The reader should consult the original references and follow the verification and validation processes adopted by your company / institution when carrying out engineering calculations and analyses. Fluid Mechanics 101 and Dr. Aidan Wimshurst are not accountable or liable in any form for the use or misuse of the information contained in this talk beyond the specific educational and demonstrative purposes for which it was intended.