Channel Title: Fluid Mechanics 101 Channel Description: Fluid Mechanics 101 is a channel dedicated to bringing you up-to-date, scientifically validated discussions in fluid mechanics. Computational and numerical methods are covered extensively, with a focus on modern, commercial and academic codes. At all times, methods and discussions are referenced correctly, with open-source links provided where possible. The channel aims to be a reliable and convenient source of information for scientists, engineers, academics and researchers, so that formulae, methods and data can be accessed quickly, avoiding hours spent digging though textbooks and research papers to locate a single formula! As the channel aims for information to be convenient, videos are deliberately kept short and concise. All suggestions for new video topics/clarification/error spotting are welcome and strongly encouraged and can be posted in the comments section or sent to FluidMechanics101@gmail.com. Welcome to the channel. I hope you find it an indispensable resource! <video> [CFD] Meshing Guide for Pipes and Ducts (O-grid, hexcore, polyhedra) Description: An overview of different methods for meshing a 90 degree pipe bend for modern CFD codes: Timestamps 0:00 Introduction 2:32 Tetrahedral only 6:56 Tetrahedral with layers 8:58 Inefficient volume fill 15:11 Hexcore volume fill 16:19 Polyhedral volume fill 17:39 Numerical diffusion 31:45 Tetrahedral fill (revisit) 32:45 Hexcore (revisit) 34:23 Single block 37:31 Standard O-grid 40:11 Curved O-grid 42:41 Bell-shaped O-grid 46:24 Mapped approach 52:57 Outro #computationalfluiddynamics #ansa #cfd ============================================ 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. </video> <video> [CFD] Multi-Grid for CFD (Part 1): Smoothing, Aliasing and the Correction Equation Description: An introduction to the multi-grid method that is used in the majority of finite volume based CFD codes to solve sets of linear algebraic equations. Time stamps 0:00 Introduction 1:42 Example problem 3:17 Gauss-Seidel iterative solution 5:41 The iteration error 9:04 Spatial error frequencies 12:13 Coarse mesh frequencies 13:48 Aliasing 15:57 Smoothing and solving 18:28 The residual 22:37 Standard Gauss-Seidel algorithm 24:33 The correction equation 28:03 Alternative algorithm 30:37 Summary 31:47 Outro References Y. Saad. Iterative Methods for Sparse Linear Systems. 2nd edition. Society for Industrial and Applied Mathematics, 2003. isbn: 978-0898715347 C. Greenshields, H. Weller 'Notes on Computational Fluid Dynamics: General Principles', Section 5.17. 2022. https://doc.cfd.direct/notes/cfd-general-principles/multi-grid-method ============================================ 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. </video> <video> A Look Inside My New Course | The SIMPLE Algorithm Description: The early-bird discount is now closed. However, you can still get access to the course here: ********************************************************* https://dr-aidan-wimshurst-s-school.teachable.com/p/the-simple-algorithm </video> <video> [CFD] H/A (HbyA) in OpenFOAM - Part 1 Description: An introduction to the vector field H/A (HbyA) that is used to formulate the pressure equation in CFD. Timestamps 0:00 Introduction 1:26 Example mesh 2:53 SIMPLE algorithm 6:13 AU=B 8:12 Separate B 10:25 Units 14:08 Cell connectivity 16:00 Extract equation 1 20:11 H definition 22:36 Rearrange for u 24:42 Weighted-average 28:56 H/A definition 32:09 Functional notation 34:12 H/A as a vector 37:02 Summary 37:49 Outro #cfd #openfoam #HbyA ============================================ 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. </video> <video> [CFD] Pressure-based Coupled Solver (Part 1) Description: An introduction to pressure-based coupled algorithms that are used by modern CFD codes including ANSYS Fluent, OpenFOAM and ANSYS CFX to address the pressure-velocity coupling in the Navier-Stokes equations. Timestamps 0:00 Introduction 0:55 Pressure Gradient (Gauss Integration) 6:46 Face Pressure Interpolation 12:15 Example Force Calculation 15:51 Simplified Form 17:22 Segregated Algorithms (SIMPLE, PISO) 19:22 Explicit Pressure Gradient 22:38 Implicit Pressure Gradient 24:28 v Momentum Equation 27:23 Pressure Equation 29:07 Block Matrix 31:53 System Iteration 32:56 Summary 34:20 Outro Some useful references: M. Darwish, I. Sraj, F. Moukalled, 'A coupled finite volume solver for the solution of incompressible flows on unstructured grids', Journal of Computational Physics 228 (2009) 180–201. doi:10.1016/j.jcp.2008.08.027 H. Jasak, 'Coupled Flow Solution Algorithms in OpenFOAM', TOBB ETU, Ankara, 23 October 2019. #pressure-velocity-coupling #cfd #fluidmechanics ============================================ 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. </video> <video> [CFD] Pressure-based Coupled Solver (Part 2) Description: Part 2 of the lecture series on pressure-based coupled algorithms that are used by modern CFD codes to address the pressure-velocity coupling in the Navier-Stokes equations. Timestamps 0:00 Introduction 0:54 Continuity Equation 10:17 Implicit Continuity Equation 15:15 Example Problem 18:45 Saddle Point Problem 20:55 Rhie & Chow Correction 23:36 Coupled Pressure Equation 25:54 Block Matrix 26:18 Coupled vs Segregated 29:05 OpenFOAM snippets 31:13 Algorithm Choice 36:08 Summary 37:21 Outro Some useful references: M. Darwish, I. Sraj, F. Moukalled, 'A coupled finite volume solver for the solution of incompressible flows on unstructured grids', Journal of Computational Physics 228 (2009) 180–201. doi:10.1016/j.jcp.2008.08.027 H. Jasak, 'Coupled Flow Solution Algorithms in OpenFOAM', TOBB ETU, Ankara, 23 October 2019. #pressure-velocity-coupling #cfd #fluidmechanics ============================================ 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. </video> <video> [CFD] Conjugate Gradient for CFD (Part 1): Background and Steepest Descent Description: An introduction to the conjugate gradient method and other gradient descent based methods (steepest descent method) for CFD. This is Part 1 of a 2 Part lecture series. Time stamps 0:00 Introduction 2:53 Gauss-Seidel Recap 7:20 Quadratic Form 14:48 Gradient of f 19:37 Finding the minimum 24:00 General algorithm 25:53 Steepest descent method 29:50 Search direction (pk) 32:25 Search distance (alphak) 39:55 Steepest descent summary 41:33 Conjugate gradient motivation 43:02 Summary 44:33 Outro References J. Shewchuk 'An Introduction to the Conjugate Gradient Method Without the Agonizing Pain', Edition 1 1/4, 1994. https://www.cs.cmu.edu/~quake-papers/painless-conjugate-gradient.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. </video> <video> [CFD] Conservative, Advective & Material Derivative forms of the Navier-Stokes Equations Description: A basic overview of the material derivative, conservative and advective forms of the Navier-Stokes equations. Time stamps 0:00 Introduction 0:00 Introduction 0:57 Example Problem 7:56 Material Derivative 10:21 Navier-Stokes derivation 15:36 Surface and volume forces 19:36 Conservative and advective form 22:59 Derivation 27:39 Equivalence of forms 28:54 Other transport equations 31:40 Outro ============================================ 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. </video> <video> [CFD] Inflation Layers - Part 2 (Corners, Orthogonality, Smoothing) Description: An overview of the inflation layer generation process used by meshing software for CFD (Part 2). Timestamps: 0:00 Introduction 1:22 Before We Start 3:14 Node and Face Normals 4:54 Warping 9:07 90 Degree Corner 11:05 Negative Volume 12:50 Normal Vector Smoothing 14:31 Projection Distance 17:02 Crevices 21:04 Distance Smoothing 23:52 Orthogonality Problems 26:43 Mixed Approach 30:50 Example Mesh 33:22 Summary 34:30 Outro #cfd #meshing #fluidmechanics101 ============================================ 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. </video> <video> [CFD] Conjugate Gradient for CFD (Part 2): Optimum Distance and Directions Description: An introduction to the conjugate gradient method and other gradient descent based methods (steepest descent method) for CFD. This is Part 2 of a 2 Part lecture series. Time stamps 0:00 Introduction 0:50 Basic algorithm summary 3:54 Iteration error (ek) 7:06 The key idea 9:20 Orthogonal directions 10:21 Conjugate directions 12:34 Optimum distance (alphak) 15:54 Alphak derivation 20:37 Next direction (pk+1) 26:39 Slider (betak+1) 28:59 First direction (p0) 30:14 Simplifications (alphak, betak+1) 31:08 Algorithm summary 33:32 Outro References J. Shewchuk 'An Introduction to the Conjugate Gradient Method Without the Agonizing Pain', Edition 1 1/4, 1994. https://www.cs.cmu.edu/~quake-papers/painless-conjugate-gradient.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. </video> <video> [CFD] Multi-Grid for CFD (Part 2): Restriction and Prolongation Description: An introduction to the multi-grid method that is used in the majority of finite volume based CFD codes to solve sets of linear algebraic equations. Time stamps 0:00 Introduction 0:45 Recap 2:54 Agglomeration 5:17 Restriction 10:06 Restriction Example 11:48 Restriction Matrix 15:18 Prolongation 19:55 Prolongation Example 20:57 Prolongation Matrix 24:11 Coarse Mesh A Matrix 26:49 Derivation of A' 30:41 A' Example 34:12 Algebraic Multi-Grid 36:13 Summary 37:42 Outro References ------------------------------------------------------------- C. Greenshields, H. Weller 'Notes on Computational Fluid Dynamics: General Principles', Section 5.18. 2022. https://doc.cfd.direct/notes/cfd-general-principles/gamg-method Y. Saad. Iterative Methods for Sparse Linear Systems. 2nd edition. Society for Industrial and Applied Mathematics, 2003. isbn: 978-0898715347 ============================================ 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. </video> <video> [CFD] H/A (HbyA) in OpenFOAM - Part 2 Description: An introduction to the vector field H/A (HbyA) that is used to formulate the pressure equation in CFD. Timestamps 0:00 Introduction 0:36 Differential Equations 5:40 Recap of Part 1 10:28 Vector form of Momentum Equation 12:36 Continuity Equation 14:33 Pressure Equation 19:50 Source Term 21:42 Divergence Theorem 25:57 Midpoint Rule 30:20 Integrated Source Term 35:31 phiHbyA 39:03 Summary 40:09 Outro #cfd #openfoam #HbyA ============================================ 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. </video> <video> [CFD] Pipe Mesh Transitions (Unstructured, Hexcore, Block Structured) Description: A collection of methods for meshing the transition from a cylindrical pipe into a larger domain using Beta-CAE Systems ANSA. Timestamps 0:00 Introduction 1:37 Geometry 3:11 Block Structured Approach 10:22 Alternative Blocking 14:21 Improved Blocking 19:55 Unstructured Approach 26:56 Improved Surface Mesh 30:53 Mixed Structured / Unstructured 35:14 Summary and Outro #ansa #cfd #meshing ============================================ 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. </video> <video> [CFD] Turbulence Intensity for RANS Description: This talk discusses the different reference velocities that can be used in the definition of Turbulence Intensity, and the effect that this choice has on the computed values in RANS CFD. Time stamps 0:00 Introduction 0:51 Background 2:49 Typical Values 4:20 How to calculate Turbulence Intensity 8:01 Turbulence Intensity for RANS 14:18 Reference Velocity 15:33 Example Problem 19:51 Summary of reference velocity choice 20:59 Contour labels 22:04 Check your CFD code! 23:11 Velocity-inlets 26:53 Summary 27:57 Outro References CFD Online, 'Turbulence Intensity', Accessed October 2022 https://www.cfd-online.com/Wiki/Turbulence_intensity ============================================ 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. </video> <video> Course Updates | SIMPLEC and PISO Algorithms Description: If you haven't signed up for the course yet, you can sign-up here: https://dr-aidan-wimshurst-s-school.teachable.com/p/the-simple-algorithm </video>

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Fluid Mechanics 101 is a channel dedicated to bringing you up-to-date, scientifically validated discussions in fluid mechanics. Computational and numerical methods are covered extensively, with a focus on modern, commercial and academic codes. At all times, methods and discussions are referenced correctly, with open-source links provided where possible.

The channel aims to be a reliable and convenient source of information for scientists, engineers, academics and researchers, so that formulae, methods and data can be accessed quickly, avoiding hours spent digging though textbooks and research papers to locate a single formula! As the channel aims for information to be convenient, videos are deliberately kept short and concise.

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