So the interesting thing is a bit of circular logic here - we need the centroid gradients to calculate the face values (for 2nd order upwinding etc) to calculate the fluxes, but we use the face values in Green-Gauss Node / Cell-based approach to calculate the gradients at the centroid. I know Fluent does this, it just seems circular. Perhaps previous iteration values are used?
Great question. I think the general consensus is that node based is the most accurate but it is noticeably slower. So it really depends on how different they are (I.e how much). If you do a comparison of all the methods for your case you may find that the difference is small enough that you don't care, so you could just go with the fastest (cell based). But if the difference is large and you need accuracy, then node based. So .... it all depends on your case 😎
Hello sir, thank for putting this excellent vedio series on gradient schemes. Did you already made the new course which you talked about in the last minute of this vedio about unstructured mesh?
Can we use the face centre values Tf calculated by the nodal values directly instead of using it to calculate nabla(Tp) and then perform linear upwind??
Ah yes, i thought long and hard about this. If we took the face centre values directly from the nodal values then the scheme would be purely explicit (evaluated in terms of the temperatures from the previous iteration). We use nabla Tp, so that the scheme is part implicit (Tp is unknown) and part explicit (nabla Tp is known and evaluated from the previous iteration). For schemes to be stable we want them to be as implicit as possible. This is one of the reasons (amongst others) that pure upwind differencing is stable. It is completely implicit. I realise this is quite tricky. It definitely took me a long time to work it out!
@@fluidmechanics101 Thank you for your explanation! So at the start of each SIMPLE step we calculate nabla(Tp) and we use it for all the correction-iterations? This does not seem so time consuming!
Hello Dr, I just have two questions, the first one is; what is the suitable method for stuctured mesh and unsstuctured mesh ? the second is, what is the suitable method for laminar mixed and forced convection?
If you dont mind I will subscribe and watch all your movies :P Im quite interested if there is anything I am not familiar with :P Are you from U.S? How old are you btw? This is quite advanced fluid dynamics/numerical method stuff... xD
Of course! Watch all my videos, i really hope you learn lots of useful things from them 😊 fluid dynamics is quite a hard subject and im trying my best to shed some light on the most difficult aspects which arent that well explained anywhere on the internet. With better understanding, we can all do our bit to make the world a better place, in whatever field and country we are in 😄 Oh and im (currently) 27 years old and from London in the UK.
The Thomas algorithm is still good for tridiagonal matrices. Arguably the most modern algorithm for general sparse matrices is multi grid. I am thinking of doing some videos on these methods in the future 👍
Nope. Fluent is a general purpose solver for unstructured meshes, which are not necessarily tridiagonal. We can't be sure but it is likely that fluent uses multigrid for the pressure correction equation and then either PCG or Gauss Seidel (or something similar) for the other transport equations
Yes i feel like fluid dynamics is a fascinating subject that really underpins many of the most fascinating and useful phenomena in the world. It is often easy to forget, but airtravel, energy, heating, marine travel and many other fields are founded on strong principles of fluid dynamics. So yea, it is pretty cool 😄
![[CFD] What is Mesh Non-Orthogonality?](http://i.ytimg.com/vi/Dg2PwX6yxYY/mqdefault.jpg)
![[CFD] What is Mesh Non-Orthogonality?](/img/tr.png)
![[CFD] Green-Gauss Cell-Based and Node-Based Gradient Schemes](http://i.ytimg.com/vi/oeA1Bg9GqQQ/mqdefault.jpg)
![[CFD] Least-Squares Gradient Scheme](http://i.ytimg.com/vi/7ymFkxx2R_k/mqdefault.jpg)
![[CFD] The Courant (CFL) Number](/img/n.gif)
Hello Aiden ,
Very nice video as always and can't wait to see the next series of your work .
Thanks
Hai Aidan, waiting for your video...It was great, Thanks for the upload.
Thanks again Nikhil 😄
Wonderful presentation!
So the interesting thing is a bit of circular logic here - we need the centroid gradients to calculate the face values (for 2nd order upwinding etc) to calculate the fluxes, but we use the face values in Green-Gauss Node / Cell-based approach to calculate the gradients at the centroid. I know Fluent does this, it just seems circular. Perhaps previous iteration values are used?
Yes! That is the trick. You have to use the field values from the previous iteration 😃 sometimes people call this 'lagging' or 'deferred correction'
hahaha i've never looked at it that way!
Hello Aiden, based on what has been said the best choice for analysis setup is Least Squares Cell Based or Green-Gauss Node Based?
Great question. I think the general consensus is that node based is the most accurate but it is noticeably slower. So it really depends on how different they are (I.e how much). If you do a comparison of all the methods for your case you may find that the difference is small enough that you don't care, so you could just go with the fastest (cell based). But if the difference is large and you need accuracy, then node based. So .... it all depends on your case 😎
Now I understand why my simulation works ONLY with the Green-Gauss node based scheme
Useful and interesting
Thank you, it is a very useful video
Hello sir, thank for putting this excellent vedio series on gradient schemes. Did you already made the new course which you talked about in the last minute of this vedio about unstructured mesh?
Yea, it's called CFD Fundamentals 3. You can check it out on Udemy or my website (links in the description)
@@fluidmechanics101 Alright! I will register in udemy. Thank you.
Can we use the face centre values Tf calculated by the nodal values directly instead of using it to calculate nabla(Tp) and then perform linear upwind??
Ah yes, i thought long and hard about this. If we took the face centre values directly from the nodal values then the scheme would be purely explicit (evaluated in terms of the temperatures from the previous iteration). We use nabla Tp, so that the scheme is part implicit (Tp is unknown) and part explicit (nabla Tp is known and evaluated from the previous iteration). For schemes to be stable we want them to be as implicit as possible. This is one of the reasons (amongst others) that pure upwind differencing is stable. It is completely implicit. I realise this is quite tricky. It definitely took me a long time to work it out!
@@fluidmechanics101 Thank you for your explanation! So at the start of each SIMPLE step we calculate nabla(Tp) and we use it for all the correction-iterations? This does not seem so time consuming!
@@fluidmechanics101 awesome insight!
Hello Dr, I just have two questions, the first one is; what is the suitable method for stuctured mesh and unsstuctured mesh ? the second is, what is the suitable method for laminar mixed and forced convection?
wonderful!!
Hi Aiden, it is an excellent Lecture! Is there any approach we can correct the "skewness error" when we use the cell-based scheme?
Yes, I am currently looking up 'skweness corrections' but they are quite difficult to find. Will let you know when I find the answer
@@fluidmechanics101 Thank you so much. I always enjoy your lectures.
If you dont mind I will subscribe and watch all your movies :P Im quite interested if there is anything I am not familiar with :P Are you from U.S? How old are you btw? This is quite advanced fluid dynamics/numerical method stuff... xD
Of course! Watch all my videos, i really hope you learn lots of useful things from them 😊 fluid dynamics is quite a hard subject and im trying my best to shed some light on the most difficult aspects which arent that well explained anywhere on the internet. With better understanding, we can all do our bit to make the world a better place, in whatever field and country we are in 😄
Oh and im (currently) 27 years old and from London in the UK.
Hi there. can I have a demand? could you create video of most modern and parallel method to solve tridiagonal and sparse matrix?
The Thomas algorithm is still good for tridiagonal matrices. Arguably the most modern algorithm for general sparse matrices is multi grid. I am thinking of doing some videos on these methods in the future 👍
@@fluidmechanics101 Last question. even fluent uses tomas for tridiagonal matrices?
@@fluidmechanics101 Last question. even fluent uses tomas for tridiagonal matrices?
Nope. Fluent is a general purpose solver for unstructured meshes, which are not necessarily tridiagonal. We can't be sure but it is likely that fluent uses multigrid for the pressure correction equation and then either PCG or Gauss Seidel (or something similar) for the other transport equations
@@fluidmechanics101 Thank you so much.
Love you channel bro, Im working as R&D Fluid Mechanics engineer :P Do you consider it an interesting topic for youtube channel? Rgrds
Yes i feel like fluid dynamics is a fascinating subject that really underpins many of the most fascinating and useful phenomena in the world. It is often easy to forget, but airtravel, energy, heating, marine travel and many other fields are founded on strong principles of fluid dynamics. So yea, it is pretty cool 😄
Excellent presentation !