[CFD] Least-Squares Gradient Scheme

An overview of the Least-Squares Gradient Scheme, which is used by the majority of modern mainstream CFD codes (ANSYS Fluent, OpenFOAM, Star CCM etc.) The following topics are covered: 1) 3:09 How is the Least-Squares scheme different to Green-Gauss schemes? 2) 5:00 How does the Least-Squares gradient calculate the gradient at the cell centroid? 3) 17:25 An example problem 4) 22:19 Why is a weighted approach required for the Least-Squares scheme? #leastSquaresGradient #fluidmechanics101 #cfd ======================= Some useful references: 1) A. Syrakos et al. 'A critical analysis of some popular methods for the discretisation of the gradient operator in Finite volume methods' Physics of Fluids, 29, 127103, 2017. https://arxiv.org/pdf/1606.05556.pdf 2) ANSYS FLUENT User Manual 18.3.3 Evaluation of Gradients and Derivatives http://www.afs.enea.it/project/neptunius/docs/fluent/html/th/node368.htm 3) H. Jasak. 'Finite Volume Discretisation in OpenFoam. Best Practice Guide.'Chalmers University, Gothenburg, 2015. http://www.tfd.chalmers.se/~hani/kurser/OS_CFD_2015/HrvojeJasak/DiscretisationBestPractice.pdf ============================================ Want to learn more? ============================================ Grab a copy of my CFD Fundamentals Course (for beginners): https://www.udemy.com/course/computational-fluid-dynamics-fundamentals-course/?referralCode=F9CF2DFFCA224E93834E Learn how to write your own CFD code in MATLAB and python (for intermediates): https://dr-aidan-wimshurst-s-school.teachable.com/p/the-simple-algorithm Learn how I draw my figures and diagrams in Inkscape (for everyone): https://dr-aidan-wimshurst-s-school.teachable.com/p/inkscape-for-scientists-and-engineers ============================================ Did you like the video? ============================================ Download the lecture slides from my website: https://www.fluidmechanics101.com/pages/lectures.html 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): https://www.patreon.com/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.