Probably the best overall option is the so called "deferred correction" approach. Similar to your eq.9 at 30:30 , but the UD part is implicit (goes into the system matrix) whereas CD part is explicit (taken from the previous iteration). So, it will be stable like the UDS scheme is, but eventually it will recover accuracy of the CDS scheme, as it approaches convergence.

@fluidmechanics101

4 жыл бұрын

Fantastic! I have pinned the comment so everyone can see

@SamDuke474

Жыл бұрын

Seems important. But my brain doesn't understand 🤣

Real heroes don't wear capes, they explain CFD in a clear, concise and logical manner ^ ^ Your KZread channel is amazing, I will watch every single video!

@fluidmechanics101

4 жыл бұрын

Thank you so much 🥰

@user-ty6dg2zj7b

4 жыл бұрын

You just express what I think.

Words could never express how thankful I am for your lectures.

Fantastic, this in the only video ( includes text book) so far that has really explained first and second-order accuracy for FVM as its not as obvious in FDM

While I was studying in Germany, I attended CFD lectures delivered by some professors. However, I must admit that your explanations are better than theirs 😅 If I'm struggling with some CFD theory, I often turn to your channel's playlist for help.

@user-lv2ly4un4x

Ай бұрын

das stimmt!

i can just confirm what the other comments are showing : Helpful and great video. For sure CFD is wide than that...but your explanation are generally so simple and easy to understand. Thanks again and i'am looking forward for other videos

@fluidmechanics101

5 жыл бұрын

Thanks Brice, im so glad you find them useful :)

thank you sir for providing the best lecture on CFD simulations.

You are a CFD God - thank you very much for your bank of knowledge

@fluidmechanics101

2 жыл бұрын

Happy to help 😊

I love your videos and explanations! Thank you for the great work :)

Great content!! Thank you, I wish you would have more videos like this!

@fluidmechanics101

5 жыл бұрын

Great, im glad you found it useful! More videos will be coming soon, so keep watching this space :)

Thank you sir, your videos are very clear to understand, probably the best learning resource I found on the internet. Ten thumbs up from me. :))

@fluidmechanics101

5 жыл бұрын

Thank you so much Prejdak, thats such a nice comment 😊 im so glad you found my videos useful!

Brilliant brilliant work! thank you.

Really great videos you have. You go through the topics systematically and present it in a clear way with a clear language and voice. Thank you alot, you have helped me understand this topic ! Keep the good work !

@fluidmechanics101

5 жыл бұрын

Fantastic! Im so glad you like the videos 😊 i have more videos to come in future, so keep watching this space!

@dnautiyal9655

Жыл бұрын

@@fluidmechanics101 Excellent

Thanks for your videos. It's so helpful!

Dear Aidan Wimshurst, Thank you so much for your lectures. I would like to request a video on relaxation factors and how it affects the convergence rate?

Very nice video sir! The way you explain is very helpful and the logic very clear!

Thanks, very clearly explained!

Thank you for the instructive video

A very nice CFD lecture I have ever seen. 😀

Great lecture as always, Aiden! Would love to see you discuss deferred correctiom approach, convection schemes in unstructured meshes, and normalized variable diagrams (Will be rooting for a part II lecture 😂).

Thank you for that explanation.

Great video! Thank you!

Your channel is topnotch for CFD material, keep the good job and the fantastic quality of your work. BTW, I would suggest you to write a book (or smth) as an introduction to CFD. You are naturally really talented at explaining scientific topics! Salute fellow comrade.

@fluidmechanics101

4 жыл бұрын

Hi Fookas, yes i am planning on writing a CFD book ... that is actually useful 😄 it seems like all the CFD books that are currently out there just aren’t really useful. Im going to try my best to make something that we are all looking for. If you are interested, i have made a small online course to show the kind of thing im going for. You can check it out on my website. Thanks again for the support and kind words. Much appreciated 😄

Great explanation. Ty

great video, you are very clear

Very nice explanation, subscribed after seeing this video

Great work.

just one word Awesome. Thanks a lot.

You, handsome sir, are amazing. Exactly what is was looking for.

@fluidmechanics101

4 жыл бұрын

Fantastic! Im so glad 😊

Fantastic!

The best discretization schemes explanation ever Ph.D. Aidan thanks a lot. Could you make a video related to convergence criteria for complex CFD simulations like combustion and multiphase flow?

@fluidmechanics101

5 жыл бұрын

Hi Cesar, thanks for your support again! It is generally quite difficult to make a video on convergence criteria, as all simulations are different. Even the same simulation with a different mesh can produce very different convergence behaviour (especially in terms of residuals!) I think a video on general guidance for judging convergence would be a great idea though and useful for lots of people. Thanks!

29:26 According to the OpenFOAM user guide limitedLinear scheme is a linear scheme that limits towards upwind in regions of rapidly changing gradient; requires a coefficient, where 1 is strongest limiting, tending towards linear as the coefficient tends to 0. The values of limiter used are contrary to your explanation. I guess they use (1-phi) as a limiter coefficient :D

it is really helpful thanks

@fluidmechanics101

5 жыл бұрын

Fantastic! Glad you found it useful

this is great! thank you

@markfencingman

5 жыл бұрын

very impressive list of publications! congrats

@fluidmechanics101

5 жыл бұрын

@@markfencingman Thanks Marks :)

Fantastic videos as usual! As someone not too familiar with the details, I have a question: when one computes the mass flow rate at the cell face to check if F_f > 0 or < 0, how are the variables such as density and velocity (shown with a subscript f) computed? At first glance, it looks recursive.

@fluidmechanics101

5 жыл бұрын

Well spotted! The velocity and density and computed from the values of the previous iteration. This is one of the tricks of the SIMPLE algorithm and we often say that the face fluxes are ‘lagged’ (they are computed using the values of the previous iteration). I hope this helps :) you can always go and check out my SIMPLE algorithm video if you would like to know more

Thank you so much. Could you please prepare a video on dynamic mesh?

you are fabulous

Please make a video on particle injection focusing on discrete phase modelling(DPM) IF POSSIBLE

GOLD!!

Great lecture. I had a small doubt. The gradient calculation calculates the gradient at the cell centre. Let us assume that we are using Upwind scheme for face interpolation. Then the value of the upwind cell centre is transferred to the face centre. That means it is a straight line. But the gradient calculation method is calculating a value of gradient at the cell centre. So would these two values be equal? The straight line will have a gradient zero but at the cell centre we are having a different value from the gradient algorithm. Can you please clarify?

was really helpful.. thank you soo much!! can u actually make a video on different turbulent models and when to use which turbulent model??

@fluidmechanics101

5 жыл бұрын

Hi prashanth, yes definitely! I am going to a video covering the most popular turbulence models (k epsilon, k omega, k omega SST and k kl omega) early next year. Keep watching this page, they will be out soon!

Excellent content, thank you very much again! I wonder which software do you use to produce the illustrations, if possible, you can also share it with us? many thanks

@fluidmechanics101

3 жыл бұрын

I make all my images in inkscape. It is free and available on all operating systems. I would definitely recommend giving it a go, it is really good!

Thank you Aiden for your great informative videos. I have a grey area in my mind that I was wondering if you could kindly help me with. Actually, if we employ "Green Gauss Node Based" or point linear gradient scheme, the face value is calculated automatically. So in this particular case why do we still need to utilize convection schemes such as upwind or linear upwind to calculate fave value of a quantity? I would be grateful if you could help me resolve this issue. Thank you very much

@fluidmechanics101

3 жыл бұрын

Good question. The gradient schemes are used to calculate quantities explicitly (after the fluid equations have been solved) so they can be added as sources during the next time step. The upwind and linear upwind schemes are needed to discretise the convection tern and treat it implicitly (when velocity is unknown and hasn't been solved for yet). This is quite a tricky point, so let me know if that makes sense

@arminsh9315

3 жыл бұрын

@@fluidmechanics101 Thank you very much. Nice explanation. This does make sense

Is there a video about flux-vector splitting ?

Hello, thanks for the explanation. When would you use central differencing instead of linear upwind? they are both second order accuracy and linear upwind is supposed to be more robust than central

@fluidmechanics101

4 жыл бұрын

Central differencing is sometimes useful for Large EddySimulation as linear upwind can smear the solution 👍

I have a doubt regarding the nature of discretization, are they implicit or explicit, because generally we have the time step and itetation in superscript and grid location in subscript attached with discretized variables, I mean we are using P & N center data to obtain f center data but, there has to be solution update for P & N either by explicit or implicit approch, Or please correct me if I am not wrong, in FVM this solution update is done by solvers such as SIMPE, PISO, Coupled etc.

Really helpful! A quick question regarding why central differencing cannot be used for the convection term in a RANS solver but can be used to solve for the diffusion term. Why don't you get non-physical oscillations in the isolation for the diffusion term?

@fluidmechanics101

3 жыл бұрын

The easiest way to understand this is to give it a go with a simple 1D test case. You will see the oscillations start as soon as the Peclet number increases above 1. If you send me an email (FluidMechanics101@gmail.com) I will send you a free copy of my course where I go through a worked example for this. Much easier than me trying to type out a full explanation in KZread comments section ...

Hi Dr. Aidan, I'd like to say thanks for this detailed explanation on Face Interpolation schemes. 1) I have one question regarding on computing the value of Face flux, F_f using equation 4. In that equation how do we calculate the velocity vector U_f ?? In Prof.Hrvoje Jasak Thesis, equation 3.144 (page 146) ;the face flux is dependent on pressure gradient term, so do we need to guess the presure gradient term and solve the momentum equation and correct the fluxes ?? 2) And in slide number 7 for the owner cell, P we'll be having 7 equations for that right??

@fluidmechanics101

4 жыл бұрын

Hi Theja, thanks for your question. The Face flux F_f is calculated using the velocity from the previous iteration (or the initial guess). This process is called ‘lagging’ the velocity field and is the way we deal with the non-linearity in the convection term. Also, the momentum equations are calculated first using the method described here. This is called the predictor step as the momentum field does not satisfy the continuity equation and is only a prediction of the velocity field. The pressure field is calculated using the poisson equation and is then used to ‘correct the face fluxes’ (as you described. This is called the corrector step and is described in professor jasaks thesis. You could also check out my video on the SIMPLE algorithm if you are interested?

Have you considered being a professor in a university! I am studying for my final exam and this explanation is very useful. Thank you Dr. Aidan 🌹

@fluidmechanics101

5 жыл бұрын

😄 yes i am definitely going to doing some lecturing at a university in the future! I really enjoy teaching and this is something i would love to do. My plan is to also upload the lectures directly to KZread, so everyone from around the world can listen in and learn.

@killua9369

5 жыл бұрын

@@fluidmechanics101 believe me you will be the best ever in explanation! The next Feynman but in CFD 😂✌🏻

Hey Adrian , Thank you for all your previous responses . Again this video was very useful . I do have 1 question though. 1) In OpenFOAM, in the fvSchemes file , we have space for interpolationSchemes , How do you specify two different interpolation schemes for convection and diffusion terms in that section ? I've been using the default (i.e linear) which I assume it uses for all the terms. Also which scheme is recommended for the pressure term?

@fluidmechanics101

4 жыл бұрын

As far as i can remember, we specify diffusion terms in the laplacianSchemes section. Might be worth checking out the openfoam website for fvschemes as i cant quite remember 😂 yep, gauss linear is normally fine for pressure, how good is your mesh? (Non orthogonality)

@shubhamsangodkar6992

4 жыл бұрын

@@fluidmechanics101 I watched through your other videos (esp the one on non orthogonality) and did a little bit of searching myself and was able to figure out the answer. Thanks anyways

Great explanation! One question though at 15:47 : We need the blue velocity vector U_f at the face to decide how to interpolate phi to the face. But how do we get that face velocity U_f? Don't we need yet another interpolation/differencing scheme for that?

@fluidmechanics101

3 жыл бұрын

Yes. The face velocity Uf is calculated by linear interpolation from the velocity at the centroids. The reason we can do this is the velocity is known if we are solving a transport equation after the momentum equations. If we are solving the momentum equations then the face velocity is calculated using linear interpolation from the solution at the previous iteration. There is also a small Rhie Chow correction needed but I don't want to cause any confusion so won't go into this here 👍

@Hurryken

3 жыл бұрын

Thanks for the quick response!

Hello Aiden! Can you please tell me why we get a gradient that is "too steep" ( 26.39 ) ?? Thank you so much for these videos!

@fluidmechanics101

4 жыл бұрын

The gradient is calculated using all of the surrounding faces, so can result in a large value. When we interpolate across one of the faces this can result in a face value that is larger than the value of the centroids across the face. If you plot this, the result will be non-physical oscillations. I think im going to do a video on gradient limiters soon, so this should make more sense 😊

@ashuftw

3 жыл бұрын

@@fluidmechanics101 I've been watching these videos again to fresh up my memory. I had the same doubt once again lol. Thank you for clearing it up! Your channel is hands down the best learning resource for fluid mechanics

Hi Aden. How the codes handle the QIUCK scheme for an arbitrary unstructured mesh? For QUICK, we need more neighbouring mesh. For rectangular structured grids it is easy to handle. What if we have an arbitrary mesh configuration?

@fluidmechanics101

3 жыл бұрын

Good question. I haven't quite worked this out yet either. I think the method uses the gradient at the centroid to project backwards and calculate the value which would exist at the neighboring cell (if it was there). Does this make help?

@behnamdastvareh8623

3 жыл бұрын

@@fluidmechanics101 Thanks for the response. Not completely. But, it gave me a clue.

Hi, to learn more about CFD I started to write a finite difference 2D stationary incompressible Euler code in Matlab. However, I discovered that the resulting system of linear equations (resulting from discretization and linearization) is only solvable, if I use forward difference or backward difference. Central difference (which I would have prefered) leads to a singular solution matrix, which of course is not solvable. Could someone explain that to me?

@fluidmechanics101

2 жыл бұрын

It sounds like there might be a problem with your boundary conditions. I have found I get singular matrices when the boundary conditions aren't properly specified with central differencing

If I am exporting lets say a surface temperature of block. It gives me the option to report facet values. Does this mean its looking at the centroid of all the cells in that block and then applying one particular differencing scheme? If i dont select the report facet values is it then applying this scheme to the cell centroid? If that is the case what is wrong with me looking at temperatures at the cell centroid if I am looking for max temperatures?

@fluidmechanics101

3 жыл бұрын

That seems correct to me. If you ask for vertex values it will (probably depending on the code) use distance weighted interpolation from all the centroids that surround the vertex you are interested in. Remember that is a post processing operation so you don't have to use anything fancy like upwind. Straightforward distance weighted interpolation should be fine to get the vertex values. I am not sure what code you are using (or what you are doing) but it sounds like the easiest thing to do is look at the surface temperatures of each of the faces of the block and look at the contour range and then just pick off the maximum value?

@harrisroight6891

3 жыл бұрын

@@fluidmechanics101 I am using Ansys Icepak, electronic cooling design for a university project. I believe the solver is Ansys Fluent. I'm having trouble understand the different between reporting facet value versus the alternative. Is one more appropriate to use than the other in a particular scenario?

Hi Aidan! The links that you left to us to access the content that you're basing your videos isn't working. Thankful in advance!

@fluidmechanics101

4 жыл бұрын

Ahh i think this is a problem with chrome. Chrome seems to be blocking links to the fluent manual. Have you tried using edge, firefox or safari?

Another excelente vídeo Aiden, helped me so much to define the numeric schemes tô my OpenFOAM case. Just one question here: looking to the equations that compose the upwind and linear schemes, how can we conclude that the first has more stability and, the Second, more accuracy? Hope to see your reply, thank you so much for the explanation!

@fluidmechanics101

4 жыл бұрын

When you construct the matrices in the finite volume method, the upwind scheme increases the diagonal dominance of the A matrix. Hence, we know that it increases the stability of the solution. However, the variation across the cell is no longer linear, so it is less accurate than central differencing. If you have a look at my fundamentals course 1 (on mu website, skilshare or udemy) there is a simple worked example where you can try this out and see the effect on the matrices yourself if you are interested 🙃

@mateusalves9558

4 жыл бұрын

@@fluidmechanics101 Thank you for the reply. Since I can't pay right now for the course, even in the SIMPLE and PISO algoritm vídeos I didn't understand why the diagonal matrix atribute stability for the simulation. Thank you for your help!

@fluidmechanics101

4 жыл бұрын

Hi Mateus, if you send me an email (FluidMechanics101@gmail.com) i can send you the abridged version of the course for free. It has the example in it that you are looking for 😊 i never want money to be a barrier for people, so if you cant afford it just let me know and i can send you the free version. I just add a small cost to help me pay for the website running costs, journal papers etc. for running the channel.

Can You please add this Ph.D. thesis by (H.Jasak, 'Error Estimation and Analysis for the Finite Volume Method with Application to Fluid FLows', Ph.D. Thesis, Imperial College London, 1996)? This is not working for me. I want to read this topic and important for my Master's thesis. thanks in advance.

@fluidmechanics101

3 жыл бұрын

Have a quick Google search. Maybe they have changed the link? It should be available

Hi, what is this small r representing to in equation 6?is it the length btwn phiN-phif?

@fluidmechanics101

2 жыл бұрын

Yes, the vector between the centre of the face and the centroid of the cell (so xf - xP)

@kiranboddeda4121

2 жыл бұрын

@@fluidmechanics101 Thank you so much for the reply...a classic explaination, with this video I really got to know why , where and what for one must use flux limiters or slope limiters.

Thanks a lot for the video. However, I have no idea why the NS equation suddenly pops up. Hopefully, I can get your reply. Thanks in advance.

@fluidmechanics101

5 жыл бұрын

Hi Wei, the Navier-Stokes equations are there to illustrate that different discretisation schemes are used for different terms. Central differencing is used for the diffusion term and upwind differencing is often used for the convection term. These ‘terms’ also appear in other transport equations, such as the energy equation and species transport equations. I chose to use the Navier-Stokes equations as an example here as they are used in every fluid flow problem. You are right though, we could have used any transport equation as an example! I hope this helps 😊

@weili9556

5 жыл бұрын

@@fluidmechanics101 Thanks for your reply. My thought is when we are dealing with a CFD case, firstly we would solve all the conservation equations ( mass & momentum, etc)of every cell. After that, we would know all the variables ( temperature & pressure, etc) of the centroid of every cell. And then we would use spatial discretization (face interpolation) schemes to get those variables of faces. Hence, I still don't understand what spatial discretization (face interpolation) schemes have to do with all those conservation equations.

@weili9556

5 жыл бұрын

@@fluidmechanics101 Hi Aidan, hopefully, you can reply to me. U can tell me what kinds of knowledge that I should catch up with. Big thanks!!

Sir, thank you so much for your valuable videos.. I have one doubt sir, My solution is converged in first order upwind scheme. But i move on to second order upwind scheme, is not converged, and moving in straight line .,How to approach this issue.

@fluidmechanics101

4 ай бұрын

Check your mesh. Then check your boundary conditions 👍

Please make a video on Flux-Vector splitting schemes.

Hi Aidan, I just finished watching this great class. thanks a lot... your videos are always so pleasant to watch.... nothing in comparison to classic lectures... I have a question/request, how to go with schemes in OF? there are so, so many.... and all kind of keywords, cell limited comes to my mind right now... but we can choose for each variable and each numerical scheme.... it is difficult to approach de subject.... thanks a lot!

@fluidmechanics101

3 жыл бұрын

Yes, I agree with you! There are lots of different schemes and it can all get a bit confusing. My best advice would be 1) make your mesh as good as possible! An extra day of meshing can save you a lot of trouble later down the line 2) find a tutorial case that is similar to your case and use that as a starting point 3) usually simple schemes like linearUpwind and limitedLinear work pretty well unless you have a bad mesh. I would start simple and see if you can get it to work. I wouldn't try the more complicated schemes unless you really have to. I hope this helps 🙂

@francootaola9172

3 жыл бұрын

@@fluidmechanics101 thank you for your answer aidan, Yes! I am with you about the meshing the issue is that in OF is quiet difficult to "know" when you have a good mesh.... or how to improve it... snappy is not an easy tool. for example, I was having problems with my scalar transport when I had two different levels of refiment over a patch (if ther were equal, EG. 1 1 or 2 2 it worked perfectly, for 1 2 it did not work...) and I found after doing a parameter screening of the snappying dictionary that the nSmoothPatch as it increased it solved this issue (from 2 to 4), so I said myself okey...if we go up it will improve the mesh (as also even the description implies this "Number of patch smoothing iterations before finding correspondence to surface") and i went to 30, as i did not care about the time that take it and the mesh result was worse... is its quiet challenging ^^ ahaha. thanks for the advice, I will continue with green gauss and the least square videos :) best regards!

@fluidmechanics101

3 жыл бұрын

Yep, snappy is not easy! Good luck 🙂

Sorry fot one more questions. Your equations seem very nice. It is not an MS Word equation editor I think. Which equation editor is this. I am afraid it is LaTeX

@fluidmechanics101

5 жыл бұрын

Yes, all the slides are produced in latex. If you dont like the MS word equations, you can always make the equations as images using LatexIt or something similar and then import them. I hope this helps 👍

@TahsinEngin-Akademi

5 жыл бұрын

@@fluidmechanics101 Thanks a lot sir. Greetings from Turkey.

In linear upwind difference scheme, when you say gradient of phi at P, how does it compute that gradient? If that gradient is computed as (phi_n-phi_p)/deltaX, isn't it the same as central difference?

@fluidmechanics101

4 жыл бұрын

You can choose a variety of different schemes: least squares, green gauss node based or cell based (see my other videos). They are not the same as central differencing because they use the values from the previous iteration. They are explicit schemes 👍

Could you also give us a lecture about the different between K-E K-W, and LES

@fluidmechanics101

4 жыл бұрын

Yep. LES will be coming soon. For k omega, have a watch of my k-omega SST video 👍

@zhichaozhao172

4 жыл бұрын

@@fluidmechanics101 Also Reynolds stress model (RSM)

Regarding slide 10, you seem to be making the assumption that xP, xf and xN lie in a straightline. It's the case with a lattice, but it's generally not true if you have an arbitrary polyhedral mesh. How do you deal with that?

@fluidmechanics101

4 жыл бұрын

Ahh yes, you can still use the same approach. You just have to use the magnitude of the vectors connecting these points. One side effect of the points not being in a straight line are skewness and non orthogonality errors. But those are for another video 😊

@murbard

4 жыл бұрын

@@fluidmechanics101 thank you for your reply. In that case, you're no longer second order accurate though, are you?

@SomeTenth

4 жыл бұрын

@@murbard That's right. That's why non-orthogonality and skewness correctors are introduced to ensure 2nd order of accuracy. Prof. Jasak explains that nicely in his PhD thesis.

However the hybrid schemes are stable for LES.

@fluidmechanics101

4 жыл бұрын

Yep you are probably right, im not an expert at LES 😂

JODER BUENAS TARDES.

Thanks so much!!! Probably my code is unstable because i didnt use this

@carlosperalta4809

Жыл бұрын

Yeah, confirmed, it was the reason.

20:00

Oi mate, u look like elon musk lol and yes the videos are great

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