[CFD] Rhie & Chow Interpolation (Part 3): Deriving the Correction!

Fluid Mechanics 101
Fluid Mechanics 101
9.7 هزار بار بازدید - 3 سال پیش - A complete derivation of the
A complete derivation of the Rhie & Chow (1983) correction formula (sometimes called 'Momentum-Weighted Interpolation'). Rhie & Chow interpolation is used to avoid chequerboard oscillations, which arise in pressure-based solvers which use a collocated variable arrangement. The following topics are covered: 1) 04:31 Explaining the notation used in the Rhie & Chow correction formula 2) 09:55 Deriving the formula used in the Rhie & Chow correction formula 3) 28:10 How does Rhie & Chow interpolation prevent chequerboard oscillations? #RhieChowInterpolation #fluidmechanics101 #cfd ******************************************************** Note: there is a small error in the diagram on page 11. Either 'Distance 1' should refer to the distance from 'f' to 'E' or the linear interpolation formula should be the other way around: U_f = (1-l_x)Up + l_x UE. This has been corrected in the lecture slides on Patreon. ******************************************************** Some useful references 1. Bartholomew et al. 'Unified formulation of the momentum-weighted interpolation for collocated variable arrangements', Journal of Computational Physics, 2018, 375, 177 – 208. www.researchgate.net/publication/327217521_Unified… 2. Rhie and Chow, 'Numerical Study of the Turbulent Flow Past an Airfoil with Trailing Edge Separation', AIAA Journal, 21(11), 1983. www.academia.edu/24382500/Numerical_Study_of_the_T… 3. Versteeg & Malalasekeera, 'An Introduction to Computational Fluid Dynamics: The Finite Volume Method', Longman Scientific & Technical, 1995. www.amazon.co.uk/Introduction-Computational-Fluid-… 4. Ferziger & Peric, 'Computational Methods for Fluid Dynamics', 3rd Edition, Springer-Verlag, Berlin, Heidelberg, New York, 2002. www.amazon.co.uk/Computational-Methods-Fluid-Dynam… ============================================ Want to learn more? ============================================ Grab a copy of my CFD Fundamentals Course (for beginners): www.udemy.com/course/computational-fluid-dynamics-… Learn how to write your own CFD code in MATLAB and python (for intermediates): dr-aidan-wimshurst-s-school.teachable.com/p/the-si… Learn how I draw my figures and diagrams in Inkscape (for everyone): dr-aidan-wimshurst-s-school.teachable.com/p/inksca… ============================================ Did you like the video? ============================================ Download the lecture slides from my website: www.fluidmechanics101.com/pages/lectures.html Buy me a coffee to say thanks: www.buymeacoffee.com/NKEZrhvg0 Support the channel on Patreon (and get useful extras for your CFD studies): www.patreon.com/fluidmechanics101 ============================================ Donations: ============================================ 1) PayPal 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 1400/07/02 منتشر شده است.
9,770 بـار بازدید شده
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