[CFD] What is Mesh Non-Orthogonality?

[@hassannemati7331]

Man, you are the best. I have never seen such a simple and nice explanation. Thank you.

[@fluidmechanics101]

Thanks Hassan! That means a lot 😊

[@killua9369]

Nothing short of incredible ! I wish all the science community to have an endless support for you. You have the power to explain complicated things in a clear and simple way even my prof. can't do this!

[@shubhamsangodkar6992]

Adrian, what a beautiful explanation my man. We need more humans like you on earth. Praying for your good health in these difficult times. Ciao

[@ryzesupremus611]

The best of the best explanations I have ever come across.

[@lestroarmonico]

Wow, this channel is like a heaven for a fluid lover like me. Thank you very much for the great content, sir!

[@fluidmechanics101]

Thanks Yusuf 😄 im glad you like it!

[@kawsarsajib8600]

Great explanation. You have demonstrated your thorough study of the topic. I wish you all the best.

[@christianh.salinas9034]

thank you for this effort to share your knowledge with other people interesting in CFD world!

[@ThiagoParente]

Great didactics... step by step, openning the terms. Congratulations.

[@fluidmechanics101]

Thanks Thiago! Much appreciated

[@knowledgesharing5730]

you make things simpler dude!!

[@fluidmechanics101]

Thanks Kumar 😊 much appreciated!

[@rafaortwein6646]

Very useful knowledge

[@sivaaero92]

Hi Aidan. One simple word i can say is "Awesome". If someone asks what is called teaching then definitely i will quote your videos as example 🙂. Thanks a lot for these videos.. i can say no one can make it more simple than what u have made in explaining FVM. Thank u once again 😊

[@fluidmechanics101]

Thank you so much 😊 it really means a lot to me!

[@sivaaero92]

@@fluidmechanics101 u deserve more than this dear friend👍. keep up the good work.. one small request from my side. Is it possible to make a video to show how FEM is discretized and what are difference between FVM and FEM. I have a basic understanding between these 2 but just various to know how fem is dicresitized. Whereas the first priority is cfd only.. please continuity your good work. 👍👍🙂

[@MANISHSINGH-hh3wp]

your content is really good. I hope you get so much success for your youtube channel. Keep this going. You should also make videos on gradient limiters.

[@engineeringarts4509]

A good explanation about the treatment on the diffusion term. A very clear demonstration about the deposition into orthogonal and non-orthogonal terms, and the implicit / explicit treatments for the respective terms. However, it looks the reason of the separate treatments are not discussed. Much grateful if you could add some remarks on that?

[@fluidmechanics101]

Yep, this will be coming soon!

[@lorenzosalvucci9704]

Thank you Aidan! Your videos are really invaluable, because information on CFD theory is really difficult to find in an organised and easy to understand way like you explain it! In this video, I have a problem with equation 9 at 15:20. It looks to me that even if *n̂* is parallel with *d* , this does not allow any simplification of the dot product *∇Uf ∙ n̂* . This is because the orientation of *∇Uf = (Up-Un)/|d|* is given by *(Up-Un)* , and it is a generic 3D vector not necessarily parallel to *d* . Therefore, when taking the dot product *∇Uf ∙ n̂* , the angle between *∇Uf* and *n̂* still has to be accounted for . What am I missing here?

[@vigneshveeresparan856]

Very good explanation!! Made me to understand the concepts so simple. Keep up the good work.

[@frictionless]

Very informative video. Thanks.

[@fluidmechanics101]

Great, im glad you found it useful 😊

[@HeitorvitorC]

Dude, I cannot thank you enough for the content. Thank you so much for the effort you put in your work.

[@fluidmechanics101]

No problem, glad you find it useful 😊

[@ashishtiwari1912]

Your explanations are very clear. Keep making such videos. Can you make one video on cell aspect ratio. In particular, why the high aspect ratio in the Inflation layers affect results such as drag coefficients?

[@fluidmechanics101]

This is a difficult question and i am currently looking into the answer. From my own experience aspect ratio seems to have a significant affect on the pressure equation but im not sure why yet .... as soon as i find out a video will be coming! I

[@mohamedemara6906]

Amazing work. Keep it up.

[@oskarelmgren]

Are the angles associated with equation (10) correctly drawn? Around time 16:43

[@fluidmechanics101]

The unit normal vector is always normal to the face (right angle). The other two vectors can be different lengths, which result in different angles. If you watch part 2, I go through the differences between the different decompositions for the other two vectors which should help explain

[@oskarelmgren]

@@fluidmechanics101 I was expecting the normal vector being split into orthogonal and non-orthogonal components to result in them being at a right angle to each other. A "100% orthogonal", and a "0% orthogonal" component. I will definitely watch part 2 to see if I understand this correctly with the different options.

[@fluidmechanics101]

I think it is the other way around. The normal vector is always orthogonal (90 degrees) to the face. It is decomposed into a component that is parallel with the vector d, that connects the cell centroids across the face, and a residual component. This should be explained in the next video. If not I will try and add some more detail 🙂

[@jaewooklee3494]

Thank you so much for your effort :)

[@armaanmohammed8874]

Hi. A small question: For the convection term, the volume integral was appropriated to summation over each face(U*F), where U and F are the velocity and mass flux at each face. The mass flux also contains a dot product of the velocity at the face and the normal vector. Do we have the non-orthogonality treatment over there as well? Also, on slide 12, why is it U_P - U_N, and not U_N - U_P?

[@lampisspyropoulos2852]

i love you my friend... you are the best

[@nuhajn8964]

I have a question about the skewness and neighboring corrections in ANSYS Fluent. As I understand it, non-orthogonal correctors run in the background, and the user actually has no role in adjusting them. However, what about skewness errors? These corrections are actually up to the user to define, and they have to be an integer number, 1or higher. So, how do these affect the equations, and why do they only appear in the PISO algorithm

[@araceligzz]

Thanks for this video. This is so much helpful.

[@shreyasmurali4616]

Excellent video as always Dr.Aidan,but I have a doubt.Instead of calculating the gradients as explained in the video,why can't we take a weighted average of gradients in the cells which share the face. I understand that there could exist a skewness error in the same,so why not do a nodal averaging of gradients wherein the gradients at the nodes are obtained by a weighted average of cell gradients. In other words,why don't we deal with the gradients of flow variables here the way Green Gauss Node based scheme deals with the value of flow variables. Sorry if the question is very trivial.I am a beginner in the field. Could anyone please shed light on the same?? Thank you in advance

[@jialiangzhou1428]

hello, one simple question. why we need to use implicit scheme in the orthogonal component and explicit scheme for the non-orthogonal component? many thanks for answering.

[@fluidmechanics101]

We can use an implicit scheme for the orthogonal component as it is only possible to write the temperature gradient in terms on the unknown temperatures (TN and TP) when the vector d is parallel with the unit normal vector. If they are not parallel (the non-orthogonal component) then we cant do this, and we have to evaluate the dot product explicitly (using the temperature gradient from the previous iteration). This is explicit treatment. I realise that this is the most challenging part of the orthogonality treatment and it is quite confusing. So i am going to explain it in a lot more detail in my upcoming course ‘Fundamentals 3’, which will be coming out soon! You will be able to pick up a copy from my website or patreon (links in the description), whichever you prefer 😊

[@kowualsky]

Hi, I have a question. Here we replace n by delta + k. But why can't we just use the n, e.g. normal vector, of the face. From the vertices of the face, we can calculate the exact normal vector, right?

[@SuperBehrang]

Great explanation, man! tnx

[@himanshushrivastava7062]

Hello Aidan, Thank you for the videos.....Just two question.... In convection term video, we didn't worried about the orthogonality. Is thin mean, for a convective flow when there is no diffusion term, a highly non-orthogonal mesh does not cause divergence? and between skewness and orthogonality, which is better quality measure?

[@th3sci3nt1st]

Thank you again for this excellent video. In your opinion, what would be the non-orthoganality angle treshold in order to apply the corrector? Since I'm using OpenFOAM, I could set the limiter parameter 'gamma' accordingly. Lastly, I saw you mentioned that the non-ortho correction is always added in OpenFOAM. I've noticed that OpenFOAM use a 'snGradScheme' on the diffusion term (LaPlacian) and, if I understood correctly, you can choose one that apply correction via implicit and explicit term for non-ortho correction. So, how the non-ortho correction is always apply if I can choose a linear 'snGradScheme' on the diffusion term?

[@supreethsultanpur563]

Great work, incredibly helpful, Adrian! I’ve a doubt. Why is it that only pressure equation is non-orthogonally corrected while momentum and energy equations too have diffusion terms?

[@fluidmechanics101]

I've been working on this for a while and I think I need to update my explanation (it is quite tricky). We always need to add non orthogonal correctors in momentum and energy equations, or we will get errors. In the pressure correction equation, if we are solving for a pressure correction (as in traditional SIMPLE, not modern OpemFOAM SIMPLE) then the pressure correction tends to zero as the algorithm converges, so it doesn't matter if we neglect the non orthogonal source term (as long as the mesh isn't too bad). I should have more detailed info coming out for this in a few months, it is quite tricky and needs a detailed explanation!

[@supreethsultanpur563]

@@fluidmechanics101 Looking forward to that!

[@Miao_zai]

Thank you for your work!!

[@Alhussainba]

Hi, sorry a small question, how do I go about referencing the content of your video in my thesis ? do you have a book? And really thanks for the great explanations.

[@mohammadmohagheghfaghih8313]

Nice Explanation! Thanks

[@riddhideepbiswas1895]

very good explanation can u please make videos on OpenFOAM ?(especially explaining the entries of the snappyHexMeshDict)

[@fluidmechanics101]

SnappyHexMesh is a tricky one. I will be looking at it in future. However, at the moment i am trying to make CFD videos that are applicable to (almost) all codes, so that they can be useful for everyone 😄 in future, snappyhexmesh for sure! As an open source mesher, i think it is a really powerful tool that will only get better in future

[@Shri_RRaamm]

Hi Aiden Sir, I have a doubt that (Equation 13) how in case of non-orthogonal term (implicit one) velocity at cell centroid is unknown but in case of orthogonal term, velocity is known ??????????????

[@fluidmechanics101]

The velocity in the orthogonal term is calculated using the value from the previous iteration. This is why the velocity is known. Once the simulation is converged, the velocity from the previous iteration equals the current velocity and we are good 😊

[@Shri_RRaamm]

Thank you so much for enlighten me

[@jpk8588]

why not just use the Green-Gauss node based approach again but for the new gradients at the cell centers? So instead of interpolating the scalar values to the nodes we interpolate the gradients to the nodes and finally get the face averaged gradients.

[@博士维尼]

very useful for me. Thanks

[@mauriciorey9558]

Great video Dr. Aidan. I would like to ask you which book is a good one to learn about CFD using finite volume method for a beginner in the topic. Thanks

[@fluidmechanics101]

I would go with the book by Versteeg and Malalasekeera. I think it is called something like 'Fundamentals of the Finite Volume Method' 👍

[@mauriciorey9558]

@@fluidmechanics101 Thank you, you should try to make your own book

[@franky0226]

Are these also the part of your CFD fundamentals course, sir?

[@fluidmechanics101]

Not yet. I haven't included them in my current courses but maybe I will put them in a future course when I get around to writing them 😊

[@franky0226]

@@fluidmechanics101 Thank you! Your videos are the best :)🙏

[@Wow_1991]

Currently, I am searching for a job. Once I find one, I will buy that coffee.

[@knowledgesharing5730]

please do video on OpenFOAM

[@vasna92]

thanks a lot for this

[@bhanusharma8358]

thanks brother .