[CFD] Residuals in CFD (Part 1) - Understanding Residuals

[@fluidmechanics101]

Hi Everyone, I just wanted to say thank you to those of you who noticed the sign errors on Slides 6 and 7. The coefficients A21 and A23 should be - k L / Delta x. In general for the Laplacian operator, the coefficient of the diagonal (A22) should equal -1 times the sum of the other coefficients, and so the coefficients A21 and A23 should have a - sign! In Equation 1 and 2, Qsource should be negative, as the sign convention here is positive heat fluxes denote heat leaving the cell (so Qsource should be -Qsource as heat is entering the cell). For those of you who support the channel on Patreon, the PDF slides have been corrected there. For everyone else, I have pinned this post so that you are aware of the typos if you go through the derivation in your own work. Thanks again for watching the lectures and supporting the channel :) Aidan

[@jimeshpitroda937]

can you make how to study transient residuals? big thank you . you are doing great work sir

[@Hari2100]

I hope youtube provides a way to re-upload with corrections in slides to the video in a much quicker way. It helps everyone. This is because not everyone sees both videos and comments. @Aidan: It may help everyone.

[@fluidmechanics101]

Yes, me too! I haven't found a better way of doing this yet. It would be really good if there was a way of having a 'living lecture' that we can update with corrections and improvements. The best I can think of so far is to pin a comment with corrections / include the corrections in the description

[@jacks.554]

​@@fluidmechanics101 Hello there, I think that the explanation stated above could be rather misleading for someone. There are strict rules that should be followed during the calculation procedure. First, we need to specify a positive direction for the heat flux (let´s assume a positive direction for heat flowing INTO the element). Therefore, any heat flowing out of the element will have a minus sign. Then, we need to stick to the second rule which is the fact that heat flows from a higher temperature to a lower one. So, according to our specified diagram, the temperature differences should always be written as follows: (temperature at the tail of the arrow - temperature at the head of the arrow). The trick is that we can specify the directions of the arrows in the diagram arbitrarily as long as we stick to these rules. Hope it helps! Thanks for the great work!

[@mohammedtosifahmed3730]

Sir were can I get 3d navier stock equations in python

[@edoardolucianobrunetto7819]

It’s just great to see how you manage to unfold the less intuitive concepts into a super clear explanation based on understanding rather than learning definitions by heart. Keep it up man!

[@atakan716]

Your mastery over the topic is so great that everything challenging about CFD becomes easy to grasp thanks to your beautifully chosen examples during the lecture.

[@gabrielcunha1787]

What a great video!!! We brazillians are gratefully with your great explanation about residuals in CFD simulation with a clarify inglish.

[@labibbidabibbadum]

Good grief! What a perfectly wonderful explanatory video. After four years of engineering I didn't get it half as well as I got it from your presentation. Thank you!

[@AliMostafazadeAbolmaali]

Another amazing video! The way you explain the equations is truly impressive, making them easy to remember.

[@vyacheslavpetrov159]

Hello from Russia. it's really cool that you record such informative and explanatory videos, thank you very much, I really want you to release your videos more often, as they help to better understand the work of cfd code. I'm really looking forward to the second part about the residuals. thank you!

[@turuncueller]

I give you the Nobel of engineering on behalf of the CFD community. Respect!

[@sinansavaskan2132]

You are the best thing happened to CFD guys. Thanks a lot!

[@asifraj321]

Amazing lecture. Now I am able to understand what residual actually is. Thanks a lot for such a wonderful talk.

[@jk463]

Great video! I've never seen any other media(clip, text, manual, whatever) describing the basics of residuals as much as this.

[@ashishkaradage]

Your my new cfd mentor.

[@skep2825]

Really enjoying the talks on the slightly deeper theory behind the more general CFD concepts that people run into!

[@thunder852za]

Very good talk, and well explained. I like the physical intuition, it is exactly the way I interpret residuals as well. For a typical incompressible solver, the residual normally represents how 'divergence free' your flow is. For our code, we actually use both L_2 and L_inf and have relations between them to assess convergence. I am sure you will touch on this in the next parts but felt I would just add the below: Another added approach I have seen to residual normals is volume weighting. Here, every cell's residual is multiplied by the volume of the cell, and then the domain volume is divided through instead of N. This allows for small stiff cells to not hold up a simulation. This can be useful on unstructured meshes. Yet another thing to do is to divide your residual by b, this normalises the residual in a way that makes the problem less dependent on the dimensionality of the simulation. In this case, the interpretation is more along the lines of how many orders do you want to drop the residual 'relative to the starting point'. This can provide more consistent convergence tolerances being applied.

[@bhavin_patel4917]

Its is very good that someone can simplfy the complex information and present in a beautiful way .

[@tedonk03]

This is great! Finally residuals are being addressed..went through some cfd manuals but there was never really a clear explanation about what or how..thanks for the awesome video. Can't wait to see the next one

[@botonb4eg1]

Just a few words. Simply the best explanation I have ever heard! Thank you very much!

[@wallacerosendo596]

Super clear explanation! Congrats for bring to us a very useful topic in an easyful manner.

[@titox7754]

Awesome video buddy! You break down super complex concepts into easy-understanding, bearable videos! Keep it up.

[@jaswindersingh3715]

Thanks a lot Aidan. I really enjoyed the whole series. It really explains all the important nuisances one needs to know. Great work.

[@elainepenguind3481]

your crystal clear explanation just saved my day! thank you so much for the effort! :D

[@svenjaherb6001]

Best explanation I have seen on this; thank you so much!

[@ssss4391]

Brilliant how you chose a simple heat conduction problem to explain residuals. Excellent talk. Look forward to the next in the series

[@yousrajemmal13]

Many thanks for your detailed clarifications. Excited to watch the next part.

[@喬きょう-e1l]

Thanks a lot. It’s just very impressive. can't wait watching part 2 3 and 4!

[@ТимофейШкредов-и2в]

And 5, 6 and 7

[@mansourouahchialamine9477]

it was very useful to understand the behavior of residuals during execution

[@doodben]

Great video!! Your breakdowns are extremely easy to understand and implement!

[@dmitriykogan8879]

Thank you so much for such a detailed and perfect explanation!

[@joe_carlson_]

Very helpful! I have been waiting for you to make videos on residuals! Looking forward to the next videos!

[@zar5989]

As usual, great content! Thank you a lot, I’m a CFD user but thanks to you I’ve been building up some of the concepts that always slipped away from my understanding.

[@dhanushyakumarkamatam2310]

clear, concise explantion. Looking forward for the next ones.

[@TheManolis1984]

Fantastic explanation of residuals. I finally know what Φ represents. I can't wait for your residual scaling explanation (local v global)

[@sebleaf8433]

Terrific presentation, great visuals and excellent pace. Big thumbs up!

[@thippeswamyv2254]

This video made me feel just WOW! Great explanation sir. Loved it!!

[@ahmedalhusseny5795]

Thanks Aidan, I've really enjoyed it and found it quite useful.

[@nabekary]

It was a great talk indeed. Can't wait for the next parts.

[@Abuthi3]

Well organized and explained deeply. Thanks a lot.

[@mark.hates.u]

Q: In practice, what do you think is the acceptable range of representative residual values to say that you have good results in your CFD? Some papers say around 10^-4 and below for all transport parameters. Can't wait for the next parts of your lecture.

[@fluidmechanics101]

Yes, 10^-4 seems to be pretty good in most CFD solvers (just from personal experience and the experience of others). But as always ... please check other quantities to check you have convergence (forces, moments, point monitors etc). Residuals are not enough by themselves!

[@prantikdas6218]

Thank you so much for the explanation. Eagerly waiting for part II. Keep it up!

[@sanjaykumaryadav3186]

Not only useful, extremely useful.

[@86gamemachine]

What a wonderful and beautifully simple explanation! Thank you, sincerely! Eagerly awaiting for the next parts.

[@manishankaryadav7307]

Your lucid way of explanation is just awesome. When I have question like how can I get just a value for the residual that may represent residuals of each cells.? And there you explain. I do not even recognise that the video has ended. Thank you so much for your hardwork.

[@killua9369]

Wallahi this guy explains things really well! He is a master! Please consider explaining the difference in using fvSolution in openfoam, which is faster GMAC or PCG solvers, smoothers and those complicated topics 😭

[@sergniko]

I found this video very helpfull and got more understanding in that resudials mean. Going to part 2.

[@rajendrakumar-bn7ch]

Great video (part 1). Looking forward eagerly to the coming parts.

[@ashutoshsingh-et7vm]

Eagerly waiting and excited to hear your talks they are great and help me out very much in my masters studies it an request can you please make some video on Aeroacoustics cfd simulation basics

[@kimiyakasaei1661]

Thanks for this helpful video. Excited about the other parts!

[@mareksawicki9070]

Thank You Sir i finally understood what is all about. You are supertalended teacher!

[@EclecticVibe]

Just a few days back was researching the residual outputs from solvers in OF! Thank you. Can you please also consider making videos on linear solvers and compressible solves.

[@dinnaruto]

Thank you so much for the explanation. I'm used to follow what my lecturer does since he doesn't explain anything abt residual concept. Now I really understand it after watching this vid. Looking forward for Part II. Keep it up man!

[@erangoldstein4674]

Very good talk, and well explained. Thank you.

[@gsambuko]

u are just a god! Thank you for a such incredible explanation of a not so homogen information in different sources!

[@markonabiy6632]

thank you ,you are great

[@ankitdave9193]

As always thanks a lot for such a detailed explanation on residuals. Looking forward to learn more on this.

[@dawnnee267]

Thanks, Aidan, for your brilliant explanation on the practice residuals! It really helps me to understand the part of CFD!

[@NilanjanMondalbluemotions]

So enlightening talk and thank you very much

[@sarojmandal981]

Very useful video. Cleared all concepts for me.

[@EngelUniverse]

Great! It really helps to have a good understanding of what residuals mean! Thanks!

[@mahmoudelnaggar8512]

Thanks Man for the informative work, this kind of work over youtube may not be benifitial to you compared to the youtubers who provide silly content but, the gold stays gold and whatever else is whatever else. keep the good work up, we are excited for more !

[@fluidmechanics101]

Thank you so much, I really appreciate it

[@sudhanshumaurya2860]

its good to be back here learning basics of CFD, always the best and informative videos. thanks

[@r_kamalovich]

Спасибо! Жду следующее видео!

[@Millie_the_Scammer]

YOU "R" A LIFESAVER. Thank you so much.

[@divyajyotibasu3001]

Great explanation!! Looking forward to many such talks.

[@syedsammarabbas551]

Thanks for making such a brilliant video

[@basaruoz7127]

Thank You so much for this wonderful and beautifully simple explanation, Thank you, sincerely!

[@joseoswaldoc.2068]

Excelente lecture. Waiting for next videos.

[@danielmartin4995]

It’s just disappointing, that there are not all parts of your already out! Awesome how easy cou can deliver that complicated stuff in an easy manner. Thanks a lot!

[@nileshgaikwad5021]

Nicely Explained. Thanks for such informative video.

[@hahahaha-hn4qu]

awesome video couldn't have explained it better

[@alekseisorokin4723]

Thanks a lot, Aidan! It's a perfect explanation

[@benhadjiserradjdjameleddin9110]

Amazingly explained, thank you

[@MalcolmAkner]

Thank you for these lectures once again, you are such a good pedagog on this subject! There is a slight error on the slide at 4:15 where you go through the numerical calculation. The T2 term should be negative overall, following all the algebra.

[@fluidmechanics101]

... ahh a typo. Thanks for spotting!

[@gokhantasdemir891]

I found that video series really useful ,and what I would say is I have better understanding of residual plots and convergence process :) Thanks

[@fluidmechanics101]

Fantastic!

[@disinlungkamei2869]

Excellent explanation loved it

[@kshitijghormode8788]

Thanks for this amazing video. Residuals topic can be very confusing at times and it’s difficult to interpret the residual line plots. Eagerly looking forward for the subsequent parts. Also it would be helpful if you could address oscillating residual plots which I had once encountered in my CFD simulation.

[@ahmhmd1990]

Very useful indeed! Perhaps in later parts, you could talk about residuals in an unsteady simulation! (especially OpenFOAM!). Thank you!

[@zettaker2181]

Thanks for sharing! Great explanation. 🙂

[@zadnipryaniy]

Thsnk you, please continue the topic

[@cmojr1]

Excellent talk!!!

[@sudhaupadhyay8080]

thanks a lot for these valuable lessons ..

[@dmitriinesterenko8165]

Thank you very much for the explanation! 👍

[@pierro281279]

This is exactly what I needed! Thanks

[@CP-zi3eg]

Great explanation...thank you.

[@selimhandogan6693]

Thank you very much for all you taught me!

[@ryzesupremus611]

I really really appreciate your videos, these are so informative and very very helpful

[@fluidmechanics101]

Fantastic 🙂 I'm glad you are finding them useful

[@rram6062]

Thanks very much. The videos are very helpful.

[@dustin3291]

Beautifully structured presentation! Thank you so much!

[@rafaortwein6646]

Fantastic lecture, many thanks.

[@kekskekskeks112]

Fantastic video! Really helped me in better understanding those funny wobbly lines 😁

[@NicoSu13]

So glad, i found this channel, its coming to the right time as prepation for my PhD and is a wonderfull source to repeat the background of CFD and even learn new nuances to each topic. I am really looking forward to the rest of the talks and i am very exicted for your future works!

[@fluidmechanics101]

Thank you for you kind words. Good luck in your PhD thesis!

[@hanidaradkah8973]

Great video! Thank you very much for sharing this!

[@mercurial152]

thanks a lot for sharing your knowledge, I hope to see next videos soon.

[@seongjunpark6593]

this video is exactly what I want

[@gerhardbekker646]

Very good video! I am looking forward to watching the rest. Hoping that you will address oscillating residuals for steady-state computations and if it is the end of the world if it happens. I have also read that bad residuals do not always mean a bad solution. It is often better to track variables of interest, such as drag, flow rate, heat transfer rate, etc.

[@fluidmechanics101]

Yes to all of these questions!

[@abhishekgade3604]

Thank you so much!!! Wonderful quality learning possible here...

[@joaolopes9990]

Thank you sou much for explaining these concepts in a simple and understandable way. Also can you please tell ne how you make your slides look so good? How do you make thise images for the cells and plots?

[@fluidmechanics101]

Its all in inkscape 👍 (and a bit of practice)

[@ibrahimnasr5585]

That is Great Mate, really helpful cheers!

[@prakashthirunavukkarasu29]

Great presentation! I appreciate for putting in so much effort. Thank you!

[@uttamcp5016]

Really usedful video! Thank you. In case of SIMPLE algorithm (say in OpenFOAM), what does the pressure residual physically mean? Is it the imbalance of the pressure Poisson equation? In which case, would it represent an imbalance in force?

[@fluidmechanics101]

This is actually a fairly tricky question. In classical implementations of the SIMPLE algorithm (that solve a pressure correction equation rather than an equation for the pressure), the residual directly represents the mass error in a given cell (i.e the sum of the mass flow rates across the faces of the cell equals the residual which should tend to zero). However in OpenFOAM, an equation is solved for pressure rather than the pressure correction. Hence, it is slightly different but I still tend to think of it as the mass error in a given cell, just because it is easier for my understanding (Notice that it is a scalar equation, not a vector equation, so the residual cannot represent a vector quantity like force. Mass however is a scalar)

[@mohamedsalem3671]

you're amazing ... one million thumbs up