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
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.
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
@@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!
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!
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.
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!
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!
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.
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
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.
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!
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
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.
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.
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!
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!
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 !
Do you have a video focussing on how iterative methods get to the correct result? How does an iterative solver solve Ax=b for example, and why would it converge to some value and not just spit out random results in every iteration?
For this we would need to look at the solvers themselves (Gauss Seidel, conjugate gradient, algebraic multigrid). I haven't had a chance to make videos on these yet. In the meantime, you could always check out the wiki for these solvers?
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?
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.
Thank you. This is a very useful video to have a deep understanding of the CFD. But I have a question, could you tell me if we have the equations for AT=B and solve the vector T. Why we still have residuals when we go back to calculate the AT-B?
You calculate the residual AT-B using T from the previous iteration, before solving AT=B. Of course, when you solve AT=B the residual will be close to zero when you solve it, as you pointed out ☺️
@@fluidmechanics101 Thanks for your answer. But I am still confused. For example for the first iteration, using the AT=B to solve the first T1 vector. And for the second iteration, using the T1 vector to solve the AT1-B to get the residuals. Is that process right? If yes, what has changed so that makes AT1≠B, Since the T has been solved by the equations in the first iteration? :)
Yes you are correct. In the case we looked at here, the system is linear and there is no real need for iteration. In a real system you may have non linear conductivity or you may have a flow field which is affected by buoyancy forcing from the temperature field. Indeed for most fluid systems convection carries most of the heat transfer and conduction is small, so the residuals might change significantly while the flow field is still updating
@@fluidmechanics101 Thank you! Now i understand it, the real system usually can't be solved easily so that we need to use the iteration to approximate like for example Gauss Seidel Methods. Your videos are very useful and I will keep watching it. I hope more and more people can watch your videos!
Please, one question. If the heat source inside the bar FV 2 is a nonlinear problem, why do you use a linear equation solver to solve the temperature matrix?
Normally we have to solve a set of equations (not just the energy equation) together. For stability we locally linearise each equation and then proceed slowly using relaxation/ time stepping. Non linear solvers tend to be more expensive (particularly computing that determinant) and the set of equations are all non linear together
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.
![[CFD] Residuals in CFD (Part 2) - Scaling](http://i.ytimg.com/vi/YXElSo3Zdzk/mqdefault.jpg)
![[CFD] Residuals in CFD (Part 2) - Scaling](/img/tr.png)
![[CFD] Hexcore Meshes for CFD](http://i.ytimg.com/vi/59xfM0ayFE0/mqdefault.jpg)
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
can you make how to study transient residuals? big thank you . you are doing great work sir
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.
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
@@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!
Sir were can I get 3d navier stock equations in python
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!
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.
You r my new cfd mentor.
I give you the Nobel of engineering on behalf of the CFD community. Respect!
Super clear explanation! Congrats for bring to us a very useful topic in an easyful manner.
thank you ,you are great
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!
You are the best thing happened to CFD guys. Thanks a lot!
What a great video!!! We brazillians are gratefully with your great explanation about residuals in CFD simulation with a clarify inglish.
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!
Awesome video buddy! You break down super complex concepts into easy-understanding, bearable videos! Keep it up.
Another amazing video! The way you explain the equations is truly impressive, making them easy to remember.
Not only useful, extremely useful.
Amazing lecture. Now I am able to understand what residual actually is. Thanks a lot for such a wonderful talk.
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.
Thanks a lot Aidan. I really enjoyed the whole series. It really explains all the important nuisances one needs to know. Great work.
Best explanation I have seen on this; thank you so much!
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
Really enjoying the talks on the slightly deeper theory behind the more general CFD concepts that people run into!
Many thanks for your detailed clarifications. Excited to watch the next part.
Great video! I've never seen any other media(clip, text, manual, whatever) describing the basics of residuals as much as this.
Brilliant how you chose a simple heat conduction problem to explain residuals. Excellent talk. Look forward to the next in the series
Great video!! Your breakdowns are extremely easy to understand and implement!
Its is very good that someone can simplfy the complex information and present in a beautiful way .
Very helpful! I have been waiting for you to make videos on residuals! Looking forward to the next videos!
Terrific presentation, great visuals and excellent pace. Big thumbs up!
It was a great talk indeed. Can't wait for the next parts.
clear, concise explantion. Looking forward for the next ones.
your crystal clear explanation just saved my day! thank you so much for the effort! :D
Thanks for this helpful video. Excited about the other parts!
Well organized and explained deeply. Thanks a lot.
Great video (part 1). Looking forward eagerly to the coming parts.
Just a few words. Simply the best explanation I have ever heard! Thank you very much!
Thanks a lot. It’s just very impressive. can't wait watching part 2 3 and 4!
And 5, 6 and 7
Great! It really helps to have a good understanding of what residuals mean! Thanks!
Excelente lecture. Waiting for next videos.
it was very useful to understand the behavior of residuals during execution
Thanks Aidan, I've really enjoyed it and found it quite useful.
Thank you so much for the explanation. Eagerly waiting for part II. Keep it up!
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.
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!
Excellent explanation loved it
Great explanation!! Looking forward to many such talks.
Thank you so much for such a detailed and perfect explanation!
Very useful video. Cleared all concepts for me.
As always thanks a lot for such a detailed explanation on residuals. Looking forward to learn more on this.
I found this video very helpfull and got more understanding in that resudials mean. Going to part 2.
This video made me feel just WOW!
Great explanation sir.
Loved it!!
What a wonderful and beautifully simple explanation! Thank you, sincerely!
Eagerly awaiting for the next parts.
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
Very good talk, and well explained. Thank you.
Fantastic explanation of residuals. I finally know what Φ represents. I can't wait for your residual scaling explanation (local v global)
awesome video couldn't have explained it better
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.
... ahh a typo. Thanks for spotting!
Thanks a lot, Aidan! It's a perfect explanation
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.
So enlightening talk and thank you very much
thanks a lot for these valuable lessons ..
Thanks, Aidan, for your brilliant explanation on the practice residuals! It really helps me to understand the part of CFD!
Thank You Sir i finally understood what is all about. You are supertalended teacher!
u are just a god! Thank you for a such incredible explanation of a not so homogen information in different sources!
its good to be back here learning basics of CFD, always the best and informative videos.
thanks
This is exactly what I needed! Thanks
Спасибо! Жду следующее видео!
Nicely Explained. Thanks for such informative video.
Amazingly explained, thank you
Thanks for making such a brilliant video
Great explanation...thank you.
Thanks for sharing! Great explanation. 🙂
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!
Excellent talk!!!
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!
Thsnk you, please continue the topic
thanks a lot for sharing your knowledge, I hope to see next videos soon.
Great explanation Bro…
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 !
Thank you so much, I really appreciate it
Great work!
That is Great Mate, really helpful cheers!
I really really appreciate your videos, these are so informative and very very helpful
Fantastic 🙂 I'm glad you are finding them useful
Do you have a video focussing on how iterative methods get to the correct result? How does an iterative solver solve Ax=b for example, and why would it converge to some value and not just spit out random results in every iteration?
For this we would need to look at the solvers themselves (Gauss Seidel, conjugate gradient, algebraic multigrid). I haven't had a chance to make videos on these yet. In the meantime, you could always check out the wiki for these solvers?
excellent video! so easy to understand! thanks so much for all your videos :)
Fantastic lecture, many thanks.
Good info on type of norms
Beautifully structured presentation! Thank you so much!
Very useful indeed!
Perhaps in later parts, you could talk about residuals in an unsteady simulation! (especially OpenFOAM!).
Thank you!
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?
Its all in inkscape 👍 (and a bit of practice)
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.
Thank You so much for this wonderful and beautifully simple explanation, Thank you, sincerely!
Great video! Thank you very much for sharing this!
Thank you very much for all you taught me!
Fantastic video! Really helped me in better understanding those funny wobbly lines 😁
I found that video series really useful ,and what I would say is I have better understanding of residual plots and convergence process :)
Thanks
Fantastic!
YOU "R" A LIFESAVER. Thank you so much.
Great presentation! I appreciate for putting in so much effort. Thank you!
Thanks very much. The videos are very helpful.
you're amazing ... one million thumbs up
Thank you. This is a very useful video to have a deep understanding of the CFD. But I have a question, could you tell me if we have the equations for AT=B and solve the vector T. Why we still have residuals when we go back to calculate the AT-B?
You calculate the residual AT-B using T from the previous iteration, before solving AT=B. Of course, when you solve AT=B the residual will be close to zero when you solve it, as you pointed out ☺️
@@fluidmechanics101 Thanks for your answer. But I am still confused. For example for the first iteration, using the AT=B to solve the first T1 vector. And for the second iteration, using the T1 vector to solve the AT1-B to get the residuals. Is that process right? If yes, what has changed so that makes AT1≠B, Since the T has been solved by the equations in the first iteration? :)
Yes you are correct. In the case we looked at here, the system is linear and there is no real need for iteration. In a real system you may have non linear conductivity or you may have a flow field which is affected by buoyancy forcing from the temperature field. Indeed for most fluid systems convection carries most of the heat transfer and conduction is small, so the residuals might change significantly while the flow field is still updating
@@fluidmechanics101 Thank you! Now i understand it, the real system usually can't be solved easily so that we need to use the iteration to approximate like for example Gauss Seidel Methods. Your videos are very useful and I will keep watching it. I hope more and more people can watch your videos!
Please, one question.
If the heat source inside the bar FV 2 is a nonlinear problem, why do you use a linear equation solver to solve the temperature matrix?
Normally we have to solve a set of equations (not just the energy equation) together. For stability we locally linearise each equation and then proceed slowly using relaxation/ time stepping. Non linear solvers tend to be more expensive (particularly computing that determinant) and the set of equations are all non linear together
@@fluidmechanics101 Thanks for the help. Excellent content.
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.
Thank you very much for the explanation! 👍