[CFD] Rhie & Chow Interpolation (Part 1): Chequerboard Oscillations
17.6 هزار بار بازدید -
3 سال پیش
-
An introduction to Momentum Weighted
An introduction to Momentum Weighted Interpolation (often referred to as Rhie & Chow Interpolation), a method which is used by many modern CFD codes to address chequerboard oscillations in pressure-based solvers which use a collocated variable arrangement. This talk is Part 1 of a 3 Part lecture series. The focus of Part 1 is understanding chequerboard oscillations and why they can occur in CFD solvers that use a collocated variable arrangement.
Timestamps:
1) 02:34 A recap of the finite volume method and the discretisation of the momentum equation
2) 23:44 What are chequerboard oscillations?
3) 41:50 What are the potential options for removing these oscillations?
#RhieChowInterpolation #fluidmechanics101 #cfd
********************************************************
TYPO: Note there is a small typo in Equation 26.
pe = 1/2 (pE + pP) pw = 1/2 (pP+pW)
The (-) should be (+)
********************************************************
Some useful references:
1. Rhie and Chow, 'Numerical Study of the Turbulent Flow Past an Airfoil with Trailing Edge Separation', AIAA Journal, 21(11), 1983.
https://www.academia.edu/24382500/Num...
2. Bartholomew et al. 'Unified formulation of the momentum-weighted interpolation for collocated
variable arrangements', Journal of Computational Physics, 2018, 375, 177 – 208.
https://www.researchgate.net/publicat...
3. Versteeg & Malalasekeera, 'An Introduction to Computational Fluid Dynamics: The Finite Volume Method', Longman Scientific & Technical, 1995.
https://www.amazon.co.uk/Introduction...
4. Ferziger & Peric, 'Computational Methods for Fluid Dynamics', 3rd Edition, Springer-Verlag, Berlin, Heidelberg, New York, 2002.
https://www.amazon.co.uk/Computationa...
============================================
Want to learn more?
============================================
Grab a copy of my CFD Fundamentals Course (for beginners):
https://www.udemy.com/course/computat...
Learn how to write your own CFD code in MATLAB and python (for intermediates):
https://dr-aidan-wimshurst-s-school.t...
Learn how I draw my figures and diagrams in Inkscape (for everyone):
https://dr-aidan-wimshurst-s-school.t...
============================================
Did you like the video?
============================================
Download the lecture slides from my website:
https://www.fluidmechanics101.com/pag...
Buy me a coffee to say thanks:
https://www.buymeacoffee.com/NKEZrhvg0
Support the channel on Patreon (and get useful extras for your CFD studies):
Patreon: fluidmechanics101
============================================
Donations:
============================================
1) PayPal
https://www.paypal.me/fluidmechanics101
==================================
Disclaimer
==================================
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.
Timestamps:
1) 02:34 A recap of the finite volume method and the discretisation of the momentum equation
2) 23:44 What are chequerboard oscillations?
3) 41:50 What are the potential options for removing these oscillations?
#RhieChowInterpolation #fluidmechanics101 #cfd
********************************************************
TYPO: Note there is a small typo in Equation 26.
pe = 1/2 (pE + pP) pw = 1/2 (pP+pW)
The (-) should be (+)
********************************************************
Some useful references:
1. Rhie and Chow, 'Numerical Study of the Turbulent Flow Past an Airfoil with Trailing Edge Separation', AIAA Journal, 21(11), 1983.
https://www.academia.edu/24382500/Num...
2. Bartholomew et al. 'Unified formulation of the momentum-weighted interpolation for collocated
variable arrangements', Journal of Computational Physics, 2018, 375, 177 – 208.
https://www.researchgate.net/publicat...
3. Versteeg & Malalasekeera, 'An Introduction to Computational Fluid Dynamics: The Finite Volume Method', Longman Scientific & Technical, 1995.
https://www.amazon.co.uk/Introduction...
4. Ferziger & Peric, 'Computational Methods for Fluid Dynamics', 3rd Edition, Springer-Verlag, Berlin, Heidelberg, New York, 2002.
https://www.amazon.co.uk/Computationa...
============================================
Want to learn more?
============================================
Grab a copy of my CFD Fundamentals Course (for beginners):
https://www.udemy.com/course/computat...
Learn how to write your own CFD code in MATLAB and python (for intermediates):
https://dr-aidan-wimshurst-s-school.t...
Learn how I draw my figures and diagrams in Inkscape (for everyone):
https://dr-aidan-wimshurst-s-school.t...
============================================
Did you like the video?
============================================
Download the lecture slides from my website:
https://www.fluidmechanics101.com/pag...
Buy me a coffee to say thanks:
https://www.buymeacoffee.com/NKEZrhvg0
Support the channel on Patreon (and get useful extras for your CFD studies):
Patreon: fluidmechanics101
============================================
Donations:
============================================
1) PayPal
https://www.paypal.me/fluidmechanics101
==================================
Disclaimer
==================================
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.
3 سال پیش
در تاریخ 1400/05/02 منتشر شده
است.
17,609
بـار بازدید شده