[CFD] Pressure-based Coupled Solver (Part 2)

Рет қаралды 4,884

Күн бұрын

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):
www.udemy.com/course/computat...
Learn how to write your own CFD code in MATLAB and python (for intermediates):
dr-aidan-wimshurst-s-school.t...
Learn how I draw my figures and diagrams in Inkscape (for everyone):
dr-aidan-wimshurst-s-school.t...
============================================
Did you like the video?
============================================
Download the lecture slides from my website:
www.fluidmechanics101.com/pag...
Buy me a coffee to say thanks:
www.buymeacoffee.com/NKEZrhvg0
Support the channel on Patreon (and get useful extras for your CFD studies):
/ 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.

Пікірлер: 42

@yavuzaks1348 7 ай бұрын

Most of KZfaqrs do not provide such valuable information about solvers, especially useful what solver to choose considering different cases. Thanks

@user-xv5xe8fo7n Ай бұрын

Thank you sincerely for your lectures! Wish we had such teachers.

@teodorbabic8007 7 ай бұрын

Looking forward to a video on density-based solver! Great job!

@berkaysimsek3011 5 ай бұрын

Such a clear and brilliant explanation. Thank you for your amazing effort! Looking forward to video on density based solvers.

@prasanthvemula_nv 7 ай бұрын

Thanks brother. I was solving the exact same problem in microfluidics using mixed convention. Your video are helping a lot for me and my college mates.

@gaetanjamet1477 2 ай бұрын

Saved my day !!

@giovannicaramia859 7 ай бұрын

As always, good job!👍🏻😎

@mahmoudsaleh9006 7 ай бұрын

Thank you so much for such amazing explanation, not only for this session but all your videos. I would suggest a new topic if you do not mind, it the grid generation. The gird generation techniques, algebraic or elliptic grid generation, are explained briefly in the references. Also they did not provide sufficient- worked examples.

@user-us9wd3un7t 7 ай бұрын

Thank you for your valuable content 👏

@mohamadfawaz4146 3 ай бұрын

Fantastic !

@hungnguyenthanh8833 7 ай бұрын

You are really genius 🙂🙂🙂. I hope that you can offer many more lectures

@is-ig4zh 7 ай бұрын

Thank you Dr!

@user-kg2rp9hu1e 6 ай бұрын

Hello Aidan, I can't believe you give these lectures for free!! Thank you very much. I have a question, is there a need to update your FVM playlist, are there any other videos beside those 10 that need to be added?

@Jialei-dw3li 7 ай бұрын

Thank you Aidan, by combining the coupled algorithm and pseudo-transient method, I think I more or less grasp the essence of the so-called coupled flow solver used in many commercial CFD software (e.g. Star CCM+ and Fluent).

@fluidmechanics101 7 ай бұрын

Fantastic. I don't think we will ever know all of the details, but at least we have enough understanding to know which solver is which!

@franciscoxaviergonzalezrom4648 7 ай бұрын

Thank you!

@roopakbaliyan5935 7 ай бұрын

Best.

@derekmitchell209 Ай бұрын

Great video! Thank you for making this series. I noticed an error in equation 14 (around the 15 minute mark). The face area (A_f) has been dropped from the last two terms.

@rccabrales 7 ай бұрын

Excellent video, thank you for the great job...I suggest a similar video but using the projection method introduced independently by Chorin and Temam at the end of the 60s.

@minjoong6687 6 ай бұрын

Thanks alot for the great lecture Sir! One qustion please. The matrix shown when you mention about 'Saddle point problem', seems not to have that problem if continuity equation goes on the top of the matrix. (I mean, if the unknown's order is P-u-v from the top.) Is there any method of resolving the saddle point problem like this? - Best regards from South Korea.

@Random-sm5gi 7 ай бұрын

Hi! Can you touch on the topic of “particle cloud” in the context of Lagrangian modeling?

@xiasuyang6556 7 ай бұрын

Does the coupled solver also treat RANS variables and passive scalars implicitly?

@meenakahimalhan2499 4 ай бұрын

very informative video, thanks, could you please make a video how CFD codes calculate lift and drag forces over vehicle or airfoils.....

@kohinoor9070 6 ай бұрын

Great video! Can you plz make a video on GEKO model as it is turning out to be new standard for turbulence modelling. Thank you.

@ThetZin-xw3zg 5 ай бұрын

😍😍😍

@mariarosales3535 6 ай бұрын

Thanks sir for the lecture. Does the use of either coupled or segregated solver's, even when achieved monotonic convergence in steady, can result in different solutions for the same simulation conditions? It's somehow to know if fields would end up to have drastical difference between them when using one or another

@fluidmechanics101 6 ай бұрын

Difficult to say. I suppose this would depend on what CFD code you are using and how rigorously they have checked it 😀 in theory they should be the same of course ..

@jacks.554 7 ай бұрын

A very nice video! I think there is an error in Eq. (8), (9). The weighting coefficients omega and (1 - omega) should be swapped. Thanks, Aidan ;-)

@fluidmechanics101 7 ай бұрын

Well spotted. Thank you!

@hcelik 7 ай бұрын

Do you have access to the "H. Jasak, 'Coupled Flow Solution Algorithms in OpenFOAM', TOBB ETU, Ankara, 23 October 2019" reference? It could be nice if you may share with me. Thanks.

@snared_ Ай бұрын

guess not?

@pablogarcia5094 7 ай бұрын

Hi, Aidan/all. Is there a good reference text book that I could use to understand pressure based coupled solvers that also discusses the effects of compressiblity? The CFX theory guide has very limited information about how compressibility is treated in the form of linearizing the (rho*velocity) term by recasting it in the fully implicit form, but that does not help me understand the concept very well. Appreciate any guidance with the above. Thanks.

@fluidmechanics101 7 ай бұрын

Sadly I don't think there are any good sources besides the user manuals. If you find any, please let us all know!

@pablogarcia5094 7 ай бұрын

@@fluidmechanics101 Will do. Thank you for all your work!

@pablogarcia5094 7 ай бұрын

@@fluidmechanics101 Getting back to the above exchange on the treatment of compressibility in pressure-based coupled solvers, I did some looking up, and found that a lot of work has obviously been done in here outside of CFX. I will mention two references below, and hopefully anyone interested can snowball from there. "A coupled pressure-based computational method for inompressibe/compressible flows", Chen, Z.J and Przekwas, A.J is more of a reiteration of the numerical discretization presented in the CFX manual, but offers some additional clarity on the treatment of the convective flux term. However, I found "The segregated approach to predicting viscous compressible fluid flows" by Van Doormaal, J.P, et al. more informative in terms of understanding the purpose of linearizing the mass flow term. After some reading, my understanding of the treatment of compressiblity in pressure-based coupled solvers is the following -- the Rhie-Chow discretization of the advecting velocity term introduces the pressure coupling (as is elaborated on in this video). Meanwhile, the density is linearized in terms of pressure in a manner that introduces the compressiblity which is evaluated isothermally. This results in formulating an equation for density in terms of the pressure from the current and new timestep. The above two terms (velocity and density) when plugged into continuity equation, and linearized in a standard manner, now produce the new diagonal and off-diagonal coefficients for the pressure equation that satisfies the hydrodynamic system while also accounting for the necessary compressibility in the flow. I hope I have been clear in my summary. Please feel free to critique my interpretation if you find something wrong about it. Thanks.

@fluidmechanics101 7 ай бұрын

Great findings! Thank you for sharing

@robbiewilliamson9783 4 ай бұрын

In many of these videos it states that we should remember that all of the flow variables vary linearly across the cell face. Could you point me towards a video where you discuss why this is the case? Thanks (brilliant videos)

@fluidmechanics101 4 ай бұрын

It's a feature of the 2nd order finite volume method. If we assume that the flow variables vary linearly across the face, then the integral across a face is equivalent to the value at the face centre multiplied by the face area. (This is sometimes called the midpoint rule). It's a neat trick that lets us convert all face integrals into the value at the centre multiplied by an area (an algebraic equation, rather than an integral). So it is the feature that ultimately allows us to convert all of our equations into matrix form (linear algebraic equations) and then solve them, but it isn't explicitly stated anywhere.

@robbiewilliamson9783 4 ай бұрын

Ah, great. That makes sense. Thanks! @@fluidmechanics101

@franciscoxaviergonzalezrom4648 7 ай бұрын

Sir, how could I contact you?

@fluidmechanics101 7 ай бұрын

fluidmechanics101@gmail.com