[CFD] The Courant (CFL) Number

[@maged779]

What is amazing is that I have very little knowledge in CFD, yet I was able to fully understand this video and your explanation. Well done, really! Good teacher!

[@PeterJang]

I learned CFD on the job. So many of these topics, including CFL (Co #), was explained to me in not such easy manner. You however explained it so well and helped me so much. Keep up the great work!

[@winstonong9593]

A Clear, Concise, and Comprehensive explanation of the Courant number. Bravo!

[@eb89367]

This guy is a gift.

[@upekaweerasekara332]

I honestly haven’t seen anything more valuable than these set of videos in whole internet. I just don’t know where to find all these complicated theories this easily in one place. Your service must be immensely appreciated 👌

[@marianzastawny156]

Really nice video. Excellent job in explaining what CFL is. I think the video would benefit from a sequel, where difference of CFL in steady and unsteady problems is discussed. Also there is a difference in implicit and explicit methods which impact the stability.

[@BiplabAdhikary]

This is a real gem. The best channel for Fluid Mechanics. Thank you very much. ❤️

[@jesuspereira4233]

This lecture was great! I´m currently learning more about transient and steady state CFD simulations, and I did not know the meaning of the Courant number that well. This video was very helpful, I could said that it is better that some of the university courses that I have taken. Congrats and thanks for the help!

[@gryphonflamingo141]

Best lecture of courant number I've ever seen.

[@fahadaslam2011]

Absolutely amazing, very well explained 👏🏻👏🏻

[@mauriciorey9558]

What a great explanation for this topic, I was able to understand every second of this video. Hopefully, all cfd books were as understandable as this. Thank you.

[@sarangpakankar6498]

Hello Dr. Aidan. All your videos are extremely knowledgeable. Many of the concepts which were not clearly understood during graduation got cleared by your way of in depth explanation and use of extremely simple language. I just wanted to request you that if you could make one or two videos for important Dimensionless Numbers in CFD it will be of great help. Your simplicity of explanation will give us more insight into it. Thank you.

[@fluidmechanics101]

Thats a great idea, thanks 😊

[@TheAnonJohn]

great video. I love how you combine theoretical knowledge with its application to cfd codes.

[@MalcolmAkner]

Great lecture as always, now I have a great grasp of the Courant number!

[@martinagotti1660]

You have a gift in explaining! Thank you so much!

[@upsceshort]

Really its very helpful for CFD users👍👍👍

[@lagoonbiswal9673]

Absolutely flawless presentation. Thanks a lot sir

[@manusego]

Lot of thanks, teacher. Great explanation! I LOVE the way you clarify difficult concepts👏💞👏💞👏💞👏💞

[@vivekbharti12]

Brilliant explanation. Hats off to your efforts.

[@316FOCK]

Thanks Man! I see you from Mexico! Congrats for your very useful videos!

[@amirhoseingolpeykarrad1721]

It is a very important lesson.

[@nileshgaikwad5021]

Great explanation and presentation. Thanks.

[@yasiruranaweera3888]

That absolutely a great presentation sir

[@febriyanprayoga7332]

amazing knowledge Sir, thank you!

[@user-bf7iz2tz1i]

Great explanation, thank you a lot! Very quality lesson.

[@karthikeyanpalani9387]

Fantastic Lecture.... Thanks!

[@ravikarantripathi7228]

Really very knowledgeable video. Thank you very much, we are learning a lot from you.

[@sriharisha251]

extremely useful! amazing explanator

[@dr.gordontaub1702]

Very nice presentation as always. Thank you.

[@fluidmechanics101]

Thanks Gordon 😊

[@usamaniaz2981]

I always thought how courant no. Is calculated in 3D, now I know.. Thanks to you Aidan.. Impressive talk. I have a request, can you make a video on relaxation factors which we use OpenFOAM?

[@SKKarthick12]

Wonderful presentation!

[@manishankaryadav7307]

Thank you again for the quality content.

[@phutanesiddheshrajan2253]

Wonderful presentation ..

[@ashutoshsingh-et7vm]

Great video sir waiting for your videos like any tv series but sir still waiting for blockbuster on large eddy simulation

[@fluidmechanics101]

... im working on the LES video right now 😄 it should be out in a few weeks time!

[@jaewooklee3494]

This lecture was great help for me!! Thank you so much :)

[@TheDaniel96314]

thank u, gretings from mexico

[@Ayush.Bhagat]

Much needed information. Thanks

[@waynezeeman8948]

Brilliant presentation...thanks

[@aryanmishra5591]

You are simply the best. Thank you!!!

[@aravindm8512]

God level Explanation

[@maysamir8106]

you are great teacher .thanks a lot

[@shubhamphysicist]

Clean and precise

[@mechtorious]

Very very good content. Thankyou.

[@pauljnellissery7096]

What a lecture!

[@jloudefonty3231]

Clearly explained, thank you

[@prabup3114]

Thanks Aiden..

[@cronos864]

Thanks for the incredible video

[@childhoodforever223]

Thank you so much sir 🙏

[@itssachink]

Thanks Man.. You are Great! Much need this one.😊❤

[@SagarKumar-ks8me]

Excellent delivery! This happens when you know the shit you talk about. Thanks man.

[@nageshjamge1372]

Great, thank again..

[@sinangoren4803]

ı understood that if the cfl number is higher than 1, it's already exceed the mesh that we are observing. But in turbomachinery you r reccomendations is less than 80. with that way how we gonna sure that these numbers are good for our cfd. I mean what might be coused if our turbomachinery cfl number is about 100. btw awesome presentation, thank you aidan :)

[@fluidmechanics101]

Yes, i probably should have explained this a bit better. In an ideal world we would always have CFL < 1. However for turbo-machinery in particular, this can be realllly slow ... so to get around this we use larger time steps (CFL > 1) and do more convergence within a time step. Really the solution is more of a series of steady state soluttions rather than a true transient. I have found from personal experience that you can often push up CFL as high as 80 without it diverging. The best thing to do is experiment for yourself 👍

[@doemaeries]

So far so good. But if I set Fluent to Density-Based with absolute velocity formulation and implicit formulation under "solution methods" the courant numbe ris set to 200 as default value. How can this work when it's generally recommended to be bolow 1?

[@fluidmechanics101]

I think fluent sets the default to 200 for steady state simulations because it is using a pseudo transient formulation and can use larger than physical time steps. If you switch to transient, you can then bring the courant number down to 1 or lower

[@JohnVKaravitis]

Great video.

[@ankitjaiswal3824]

Thanks for this great video. Got to learn the basic understanding of the Courant number! I just had a doubt though: Do we need a courant number steady state CFD simulations too? Asking this I see the default Courant number listed as 5 in ANSYS Fluent for a steady state compressible flow simulation that I am doing.

[@fluidmechanics101]

For a steady state solver that uses 'pseudo time stepping' you can use whatever courant number you want, as you are trying to get to a steady state solution. However, you might find the solver diverges if you set the courant number (for the pseudo time step) too high. 5 is probably a good place to start. If it diverges, try reducing it a bit

[@ankitjaiswal3824]

@@fluidmechanics101 Yes, indeed, I am trying to run a simulation of the compressible flow through an Aerospike nozzle, and my results diverge for a Courant Number of 5. Also I happened to watch your video on 'Pressure inlet' BC. What should I take as the supersonic/ initial gauge pressure? For the compressible flow through an Aerospike that I simulating from a paper, the inlet Mach Number is close to zero in the contour plot. How close should I choose the supersonic/ initial gauge pressure with respect to stagnation pressure? I was wondering if a large deviation between those two can lead to divergence?

[@junjungarcia7236]

great job sir...

[@МаусЦзэдун]

Is the value less than 80 not an error in the calculation recommendations? That is, if I simulate a centrifugal fan, then I can specify the values ​​79 78, etc. I don't quite understand why why such large values. Thank you for the video :)

[@fluidmechanics101]

A number of around 80 is just from personal experience with OpenFOAM and the pimpleDyMFoam solver. The max value you can get away with will be different for every CFD code. I would just try some different values and see what you can get away with. I used 80 as an indicator as i havent ever really see anyone be able to get higher than 80 without it diverging ....

[@МаусЦзэдун]

@@fluidmechanics101 Thanks for the answer. I will try to use your advice and solve the problem for different values ​​of the courant number. Will try to set an automatic time step in the solver and seen what happens. Perhaps this will increase the stability of the solution when using the k-e turbulence model.

[@giabu6287]

You are saving my life

[@soroushasadian9100]

This video concerns transient analysis. I remember when I was trying to model a steady state supersonic flow over a wedge, I used the density-based solver, and in the control panel, I set the Co number to 5 according to the tutorial. Is it the same idea or not?

[@fluidmechanics101]

Slightly different. I think the solver was using a pseudo-transient to arrive at the steady state solution (a pseudo transient is similar to a transient but does not fully resolve each time step and can use different time steps in each cell). The Courant number restrictions on a pseudo transient can often be less strict than a true transient, because we only care about the final steady-state solution and not on how we get there. As long as the solver doesn't diverge, the Courant number doesn't matter for pseudo transients. I have a lecture series on pseudo transients if you would like to learn more

[@soroushasadian9100]

@@fluidmechanics101 Thank you, actually I recently watched the first part of the pseduo transient series. I thought it might be the time step in pseudo but I wasn't sure since you didn't mention it in the video Thanks again.

[@rwadalshebl7740]

Thank you very much :)

[@najikajkolaji]

great.thanks for sharing such a useful information.i have a fsi simulation in fluent part the courant number in controls section is 200 by default as my simulation is transient should i change the courant number below 1? or not?

[@fluidmechanics101]

Good question. Maybe give it a go. Does it affect your results?

[@najikajkolaji]

@@fluidmechanics101 it took so much time to solve! i set the setting back to defalt!

[@racc2218]

Thanks for give a such great explanation for CFL number. I have a question about the CFL

[@fluidmechanics101]

I think you can probably just ignore the first few time steps,as the transient is normally just washing out the initial condition then anyway 👍

[@phdmeme]

Thank you very much!

[@axelcohen8795]

Very nice and physical explanation, I really enjoyed it. However, as I recall, the importance of the CFL number was mainly due to the method for time discretization. We can't go further than 1 for explicit scheme, however the value can be much much higher for implicit scheme. Am I right ?

[@fluidmechanics101]

Yes correct!

[@axelcohen8795]

Thanks ! So why LES recommandation for CFL should be < 1 ? It doesn't only depends on the time scheme (I mean, if it is implicit we could go further without worring to much about stability) ? Thanks again to revive all my old courses :D @@fluidmechanics101

[@fluidmechanics101]

As well as stability, we also need accuracy, which is particularly important for LES. This is why we normally insist on y+ < 1

[@mehrdadkhezrian3332]

Awesome video! Please go to the population balance and polydisperse flow for the next video!

[@sheetanshudeepak8779]

Thank you sir, it was very good.

[@hughtong5551]

I just confused by the factor 0.5 at 12:40 used by OpenFOAM and only when I watch this video I get to understand finally.

[@ConnorSmithBirch]

So in Ansys, when we specify a Courant number, we are actually telling it the maximum number after which to not shorten the time steps?

[@fluidmechanics101]

I can't say for sure (as the source code is proprietary) but the idea is that the code will reduce the time step until the Courant number (either maximum or average) matches the value you specify

[@ConnorSmithBirch]

@@fluidmechanics101 awesome, thankyou!

[@ozyilmaz4269]

Thank you sir.

[@VijayaLakshmiToed]

Hi,your lecture series are great. Please tell that whether courant number criteria has to be satisfied even for implicit solver as it is stable at any given conditions?Thank you in advance.

[@ryszardb4653]

Very usefull and easy to understand interesting form of presentation. But I miss some information about optimal and desired value of Co. Maybe some future movie? I appreciate what you are doing.

[@hassanmohammadi2586]

and what about pseudo Timestep in steady state Simulation. btw it was really good

[@fluidmechanics101]

I have a nice video on pseudo time steps you could check out 👍 I'm sure it will answer your questions

[@totaloverdose3591]

Sir how do we define courant no for multiphase flows with perspective of courant no as fraction of cell travelled ?Are they distinct to each phase or sum up as a single unit?

[@fluidmechanics101]

It depends if you are using homogenous multiphase or inhomogenous. If you have a shared velocity field (homogenous) then the courant number if for both phases. If you have inhomogenous then you can have a courant number for each phase 👍

[@totaloverdose3591]

@@fluidmechanics101 Thank you sir 👍

[@RahulKumar-yk3kx]

Thankyou very much

[@mounarahal256]

Hello, do you mean by velocity fields and courant number fields the fact of plotting contours in fluent (for example for the courant number they are the coutours of cell convective courant number? thanks

[@fluidmechanics101]

Yes 👍

[@RicardoCruz-by7lv]

I don't see physical meaning for such a huge diference for Co < 80 for turbomachinery in relation to the much, much, smaller figures of other common flows. Could you explain that?

[@fluidmechanics101]

Ah yes, i probably should have explained this more. With turbo machinery it quickly becomes very expensive to use small time steps as you often need to run several full rotations of the rotor to converge the solution. Hence, it is common to use bigger time steps (so that Co is >> 1) and converge more within each time step. I have found that you can often get away with Co up to around 80 before the solution diverges. I wouldn’t stand by these values though, they are just indicative that people often go for bigger time steps with turbomachinery. I hope this helps!

[@dr.gordontaub1702]

Not sure if I am confusing this answer by putting in my two cents or not, as it has been sometime since I have written my own CFD codes and started watching these videos because I would like to get back into it. But as I recall from reading Patankar's book which introduces the SIMPLE and SIMPLER algorithms, you can sometimes get away with your code converging even with higher CFL numbers if you use a method that is more implicate than it is explicit. Although I may be confusing two different issues. As I said, it has been a long time since I read this. I was also curious about the very high CFL number listed in the video for turbomachinary, so I thank you for asking the question.

[@zaidarch]

Thank u very much!

[@Jialei-dw3li]

Dear Sir, I have a question: since the implicit temporal scheme is unconditionally stable, I can choose a large time step so that CFL can be larger than 1, am I right? In such a case, are there any constraints on the time step setting? Thank you.

[@aidealczar6075]

Hi Aidan, In the case of an airfoil, can it be assumed that as long as the lift and drag monitors are reporting constant values and the max courant number in the domain is less than 1 therefore the solution is somehow accurate?

[@fluidmechanics101]

... assuming your mesh is converged and you chosen the right turbulence model then yes 😄 to be sure of accuracy, you need to compare to experimental data

[@aidealczar6075]

@@fluidmechanics101 Thanks!

[@mathanrajk6781]

Hi! How to calculate Del.x in CFL number in ANSYS Fluent?

[@fluidmechanics101]

I think you can output CFL directly as a field, so I don't think you need to define del x

[@FILYPTC]

thank you so much bro!

[@CarlosTapiaMan]

How is the Courant number relevant for steady flows?

[@fluidmechanics101]

Only if the solver uses a 'pseudo transient' approach to achieve the steady state solution, you might need to reduce the size of the 'pseudo timestep'

[@CarlosTapiaMan]

@@fluidmechanics101 I see, I'll check out pseudo-transient flows. Thanks for the quick reply.

[@CarlosTapiaMan]

@@fluidmechanics101 As a follow up question, I've seen some Ansys tutorials of steady flow where they emphasize the Courant number setting. Usually I've seen c=5. (These are for steady compressible supersonic flows for example). I assume then this step doesn't really influence the result, since there is no flow "moving". Does that make sense? Thank you! Edit: spelling

[@fluidmechanics101]

Yes correct! If your solution is steady it does not matter how you get there as long as the calculation does not diverge along the way

[@CarlosTapiaMan]

@@fluidmechanics101 great thank you :)

[@ramgupta7697]

I am facing negative cell volume in ansys fluent what will be the possible solutions for this and in fluent I am unable to find courant number option for pressure based solver (and my mesh is unstructured-triangular). Any kind of reply is helpful, thanks in advance

[@fluidmechanics101]

Hi there. If you have negative volumes you need to go back to your mesh generator and fix the mesh. Fluent cant fix these by itself, you need to go back to the mesh generator

[@ramgupta7697]

@@fluidmechanics101 thanks for your reply. Exactly, what should I fix? Should I increase the mesh size ?

[@fluidmechanics101]

Have a look and try and find where in the mesh the cells are with the negative volume. Once you find them you need to change the mesh structure (move the boundaries, blocks, or faces) so that the cells arent inverted. You can probably find them by looking at any quality metric (skewness, non orthogonality or determinant). They should all show bad values where the cells have negative volume

[@ramgupta7697]

@@fluidmechanics101 I checked the skewness, element quality, jacobian, and aspect ratio that seem in the range. Ok I will check other parameters too btw my geometry is 2D airfoil. Thank you so much for instant reply.

[@TheAnthony761]

Hello Dr. Wimshurst. First, thank you for this presentation, explanations are very good and efficient. I would like to be sure, this stability criteria of Co < 1 is only if you solve your equations with explicit formulation and it depends also of the numerical methods we are using in the code? I mean, in some situation, even with an explicit time integration, is it possible to use Co > 1? Also, for implicit time integration, I know that there is no restrictif criteria for Co, and we can normaly use Co > 1. I'm using FLUENT right now, but I don't really understand why with implicit formulation, with a great Co, I don't have stability and my calculation diverged.

[@fluidmechanics101]

Hi Anthony, it sounds like your simulation may have diverged for another reason. Have you checked: 1) your mesh, 2) your boundary conditions ? These are often the main causes of divergence. Try solving a simpler case with the same mesh to see if you can get convergence. This will help you identify why your simulation is diverging

[@TheAnthony761]

​@@fluidmechanics101 I am trying to simulation the flow through a multi-stage centrifugal compressor and I am using the Mixing Plane Model (MPM) with mass-averaging method. The mesh is created by TurboGrid and is very good by default and the boundary conditions I have tried are Mass Flow Inlet / Pressure Outlet. I have tried also to perform with the Pressure (stagnation) Inlet / Pressure Outlet, but without success in multi-stage, when I include the MPM. Otherwise, with only one compressor stage (without the MPM model), it works...

[@aliasady2181]

awsome

[@ashutoshsingh-et7vm]

Great sir I was simulating jet impingement cooling on flatplate and consider delt t 10(-6) and max cohrent no 0.8 but my delta t reduce to 10^(-16) so i did many things it not works then I change discretion scheme of div (u) gauss cubic from gauss linear delta t adjusted to 5e-6 and cohrent no 0.24 sir does this affects my physics any way I am doing LES

[@МаусЦзэдун]

I guess not, the models remain the same

[@fluidmechanics101]

Ahh yes there could be a number of things going on here. Have you checked your mesh and run a precursor RANS simulation? Try plotting the courant number and see where it is going so high. It sounds like you have adjustable time stepping, thats why the time step is going down so much

[@egetopuzlar7836]

Hi Aidan, I follow all of your contents. Thank you for your effort. If you inform us about Adjoint solver we will be quite appreciated. Respects...

[@gokaygunduzalp270]

Thanks as a hec-ras user...

[@SwissCowboy87]

Yesssssssssssssssss!!!!!!

[@MaximumMatador]

Found this because all Thermodynamic revision seems to be done by Indian professors, which is great if you can focus your full attention on it, or speak Hindi. I wanted to do revision in the background while I serviced my bike, so I decided to review fluid mechanics instead. A bit odd, really...

[@fluidmechanics101]

I do the same sometimes 😂 the youtube thermodynamics content isnt great at the moment

[@sarangpakankar6498]

@@fluidmechanics101 nptel.ac.in/courses/112/105/112105123/ This might help for Thermodynamics. Prof S K Som is very good professor from India.

[@pattimichellesheaffer103]

GREAT series of videos! Can you say something about "stiff" interphase transport? I believe this shows up as ODE source/sink terms in a set of flow equations (one for each phase). Does this constitute and "orthogonal space" somehow - that is, can CPUs be profitably dedicated to the solution of stiff ODEs? (an example might be OF reactingFoam) Thanks!

[@fluidmechanics101]

Im not very familiar with this area but i suspect it may be due to the interface compression algorithms. These often require Courant numbers < 1 to remain stable. Sorry i cant help you out with this one

[@vm1887]

Great lecture. I have a question. The slide 'Stabilty' at 19:28 says criterion

[@fluidmechanics101]

To be honest, the criteria for turbomachinery is based on my experience with OpenFOAM. I couldnt really get a Courant number higher than 80 without it diverging. This will be different for different CFD codes and for different geometry. (Also my mesh was really high quality structured mesh, which might have helped)

[@yusufpolat13]

perfekt....

[@muhammadyasinshaikh5949]

how to get acees to cfd course for free?

[@edwardlee7579]

british boy which university do u come from

[@morrisonthomas4210]

fucking rude

[@Lilian13550]

Click on the description and you'd see Southampton and Oxford ^^

[@MaximumMatador]

Found this because all Thermodynamic revision seems to be done by Indian professors, which is great if you can focus your full attention on it, or speak Hindi. I wanted to do revision in the background while I serviced my bike, so I decided to review fluid mechanics instead. A bit odd, really...