[CFD] Large Eddy Simulation (LES): An Introduction

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Fluid Mechanics 101

Fluid Mechanics 101

Күн бұрын

Пікірлер: 291
@nikhilverma6457
@nikhilverma6457 4 жыл бұрын
That is how one teaches when he knows in and out of the stuff. Best explanation I found till now on internet. Thanks a lot.
@JesseGoossens-c4y
@JesseGoossens-c4y 8 ай бұрын
Wish all teachers were teaching stuff like this man.
@sramkumar3225
@sramkumar3225 2 жыл бұрын
Key/Important takeaways from this lecture - 1) Eddies and turbulence 2) Wave number representation of an eddy: wavenumber, k=2*pi/d, where d is diameter of the eddy 3) Larger eddies --> greater TKE, lower wavenumber 4) The energy cascade and wave number : the need to resolve atleast 80% of the turbulent kinetic energy (TKE) by a good LES 5) Integral length scale @16:58 (L0) - Single eddy with a length scale (size) that is representative of all levels of eddies present the location of interest 6) @18:10 - Mathematical equation for Integral length scale L0. 7) @19:35 - Use of steady state RANS calculation using any of the standard 2-equation models to determine integral length scale over the domain by post-processing. This forms a preliminary step. 8) @21:59 - Determining an accurate grid size based on the computed length scale. Requires nearly 5*5 cells distributed over a square of size L0*L0 9) Towards 23:40 - new parameter f to replicate the down factor of 5 from the integral scale. Shorter and more efficient way to determine the goodness of the grid resolution is to create parameter f=L0/Delta, where Delta is local cell size. So directly compute f in the initial step of TKE to judge grid.
@slim590
@slim590 Жыл бұрын
Thank you so much
@ekingorgu
@ekingorgu 4 жыл бұрын
I asked you to do a video about LES and you delivered! Best YT channel ever.
@combustionlab8081
@combustionlab8081 2 жыл бұрын
he is the best teacher for this type of stuff. ıve taken a cfd course in my licence years but it didnt come close to this video in terms of explanations.
@AshfaqUkulele
@AshfaqUkulele 9 ай бұрын
I feel ashamed to watch this genius video without paying for it. You are the Melodysheep of CFD.
@engineersacademy4137
@engineersacademy4137 3 жыл бұрын
Never found an excellent explanation for les than this. Really you are genius and deserve the best
@tejesdas3896
@tejesdas3896 2 жыл бұрын
no comment, only heart felt appreciation for the presentation! thank you so much.
@cesaaargm
@cesaaargm 3 жыл бұрын
I know for sure that those who study turbulence appreciate a lot these videos! thanks!
@sigmasix09
@sigmasix09 Жыл бұрын
The content on this channel so damn academic and wonderful. Thank you so much for your efforts and time and its really helpful for students and inspiring too👏🏼👏🏼👏🏼
@anandshankar5127
@anandshankar5127 3 жыл бұрын
Best explanation I found till now on internet. Thanks a lot for your good work
@arminkashani5695
@arminkashani5695 3 жыл бұрын
Thank you! This is an absolutely awesome video explaining complex concepts in simple terms. I realized that in the so-called "implicit" LES, as you explained here, the size of mesh dictates how fine we're able to resolve turbulent eddies. This seems to me, as a beginner to LES, to be always true. I would appreciate it if you clarify "implicit" and "explicit" in terms of LES.
@fluidmechanics101
@fluidmechanics101 3 жыл бұрын
Yes you are correct! Explicit LES is more often used in academic studies where a spectral method is used to resolve all the eddies (down to DNS range) and then the filter is applied explicitly on top of this calculation.
@nicktrindade
@nicktrindade 2 жыл бұрын
Best explanation I found till now on internet. Thanks a lot!
@taohuang5052
@taohuang5052 4 жыл бұрын
Thank you for such a detailed intro of LES! Hope to watch more lectures on carrying out LES in the future~
@sigmasix09
@sigmasix09 Жыл бұрын
Certainly yes for LES, and the explanation top notch. Thank you so much❤
@shobob29
@shobob29 4 жыл бұрын
Thank you very much for your nice explanation. When I first learnt LES by myself, I couldn’t understand why we have to consider k, but you made it clear. I would like to watch more videos about LES. Every time I watch your video, I get sth new. This is a very precious and exciting opportunity for me.
@venkatpraveengambhir6196
@venkatpraveengambhir6196 4 жыл бұрын
Excellent refresher about the concept of LES. Explaining about near-wall effects, and effects of boundary layer inflation and wall mesh sizing on resolving eddies would be even more beneficial. I am in the process of performing a turbomachinery acoustics simulation, and some pointers on those aspects would be mighty helpful.
@fluidmechanics101
@fluidmechanics101 4 жыл бұрын
Yep these will be coming soon. Im going to do the LES videos in stages as there is a lot to cover!
@ahmhmd1990
@ahmhmd1990 4 жыл бұрын
This is not just good for understanding LES, but also provides a good into to turbulence. Well done!
@refikalpertuncer8512
@refikalpertuncer8512 4 жыл бұрын
Dear Aidan, your channel has by far the greatest chance of becoming the best CFD channel there is. My recommendation is that you should slowly start to include how to implement turbulence models in CFD im terms of coding from simple to relatively complex problems, either here or on your Udemy course. Of course advanced applications should be avoided as it will be very much time consuming on your end, so just enough to give people the main idea. From there you can move forward to heat transfer, combustion, hypersonics etc..however you want. Maybe you can then move to include OpenFOAM or other software. Keep up the great work. Best regards.
@fluidmechanics101
@fluidmechanics101 4 жыл бұрын
Thanks for the advice! I will see what i can do
@TheStaticUnit
@TheStaticUnit 4 жыл бұрын
Great videos! I just started a research engineer position that's fairly CFD heavy, and your videos are a great refresher!
@venukr937
@venukr937 2 жыл бұрын
Thank you very much Adam
@nishchaytiwari8537
@nishchaytiwari8537 3 жыл бұрын
we want more LES videos. Best explaination ever.
@1321ghost
@1321ghost 4 жыл бұрын
What a fantastic lection! I'm just making my master's graduating work and this video is extremely helpful for me. More than that, your English is so clean, that it is pleasure to listen to you. Thank you from Russia!
@iloveno3
@iloveno3 3 жыл бұрын
Very nice and clear presentation. It was a pleasure to listen to you. Learned lots just in 20 min. Wished i had this at uni.
@janbrychta6278
@janbrychta6278 3 жыл бұрын
Amazing job! The clarity of your explanation is great and really helps to understand the topic. Thanks!
@pasansanjeeva3450
@pasansanjeeva3450 4 жыл бұрын
Very good introduction about LES. Waiting for more detailed discussions in the future. Better to have more details and applications of sub-grid scale models in the future.
@ivanpg5091
@ivanpg5091 4 жыл бұрын
Impressed with such a good and practical explanation! I hope you continue with your videos. They are the best on the internet!
@lenacaban4178
@lenacaban4178 3 жыл бұрын
Perfect explanation of the LES. Thank you! I'm waiting for more.
@saadmansakib01
@saadmansakib01 3 жыл бұрын
The best explanation, hands down! Thank you.
@Erickdmartinez
@Erickdmartinez 4 жыл бұрын
Would love more videos on LES! Would carry me great through my thesis!
@mohammadjadidi233
@mohammadjadidi233 3 жыл бұрын
Wonderful! I am eagerly waiting for more lectures on LES...
@edinmichael4842
@edinmichael4842 3 жыл бұрын
Thanks a lot for doing the talk on LES. Keep doing good. God bless.
@sagark9299
@sagark9299 3 жыл бұрын
Thanks a lot for this neatly done introduction to LES. Looking forward to more aspects of LES.
@PhysicsGoneBad
@PhysicsGoneBad 6 ай бұрын
Outstanding introduction to LES
@tianyiwei8825
@tianyiwei8825 4 жыл бұрын
New to LES. Interesting and seems useful and helpful. I am joining a lab where LES is used a lot but now I only have some experience using RANS and honestly speaking not fully understanding the model. I think it would be useful to see this video before going to read some papers about it.
@randomizer272
@randomizer272 4 жыл бұрын
More LES videos pls........ This is a very useful video. thank you.
@fluidmechanics101
@fluidmechanics101 4 жыл бұрын
Yes! More are coming soon 😄
@adityapahuja3129
@adityapahuja3129 4 жыл бұрын
If only i had known it earlier! Kudos on the way you showed the mesh and velocity vector, it cleared the idea so nicely! Please do post more videos❤️
@sunandamedapati4508
@sunandamedapati4508 4 жыл бұрын
Very helpful explanation. Expecting more videos on LES from your channel..thanks for giving basic and practical idea of LES.
@vimalkotak6255
@vimalkotak6255 2 жыл бұрын
Simply great again. Thank you very much
@keshavkothari5489
@keshavkothari5489 3 жыл бұрын
A nicely packed talk, hope more videos may come regarding more intresting topics. I didnt even read RANS ones but the vdo seems well informative
@velmareddyprudhwidhar7089
@velmareddyprudhwidhar7089 4 жыл бұрын
Very helpful...for a beginner like me it's a boon I found this channel
@MrHariPuthar
@MrHariPuthar 4 жыл бұрын
Thank you very much. Your videos' likes are almost 10% of the views. That's how helpful your videos are. I hope you have resources to keep up this work. I would be happy to support you on Patreon and I am sure there are lot more who would be willing to.
@fluidmechanics101
@fluidmechanics101 4 жыл бұрын
That would be great! There is a link to my patreon in the video description. I upload all of the lecture slides, courses and templates that i use onto patreon as a small thanks for supporting the channel
@Ehsaninaaa
@Ehsaninaaa 3 ай бұрын
Many thanks for such a professional teaching. Be successful ...
@abhishekshingala1212
@abhishekshingala1212 4 жыл бұрын
yes, it is useful and interesting, please don't hesitate to talk about this deeply!!! :)
@JB-nd3gk
@JB-nd3gk 4 жыл бұрын
It's amazing! You did a good job of explaining the basic concept in LES in the easiest way. Thanks!
@hafidzazharjakaria2615
@hafidzazharjakaria2615 8 ай бұрын
best LES explaination
@guilherme6535
@guilherme6535 4 жыл бұрын
Thank you a lot! Your videos are always great and, as a undergraduate in Aerospace Engineering, you make me always want more information! Greetings from Brazil
@jiabaoxing9374
@jiabaoxing9374 4 жыл бұрын
Thank you so much! Please make more videos on LES! I am so grateful!
@kenaz5985
@kenaz5985 2 жыл бұрын
Excellent material. Thank you very much
@slim590
@slim590 Жыл бұрын
Thank you, please share more on LES
@renethibault2429
@renethibault2429 4 жыл бұрын
Really nice to watch! Looking forward for more video on this topic. Thank for sharing!
@rram6062
@rram6062 3 жыл бұрын
Thanks very much for such a nice lecture. It was very informational and helpful. Excellent talk on LES!
@ManishSinghPME
@ManishSinghPME Жыл бұрын
Dear Aidan, Really well-explained video. But I have one point to raise here what you have defined as an integral length scale is actually a turbulent length scale. As mentioned in Appendix A of the paper "Index of Resolution Quality for Large Eddy Simulations".
@fluidmechanics101
@fluidmechanics101 Жыл бұрын
You may be right. I haven't read that paper
@sauravpathak2116
@sauravpathak2116 4 жыл бұрын
Great video Aiden! Love you vidoes. You are helping our community. Appreciate it. Have been familiar with LES theory from Versteeg. The basics are explained well in there too, particularly, about sub grid models; if anyone is interested. However, you wont find stuff about the integral length scale, the practical aspect. Love how you explain stuffs man. Thanks!
@emiliopelizzari3537
@emiliopelizzari3537 Жыл бұрын
Thanks for your very usefull and clear explanations
@KToMmi
@KToMmi 3 жыл бұрын
This is exactly what I was looking for. Wonderfully explained, fantastic job! Thank you!
@chiragtarsadia8681
@chiragtarsadia8681 4 жыл бұрын
You exactly post the lecture which I was looking for...thank you...and support your work. 😊
@jsqueo299
@jsqueo299 2 жыл бұрын
Awesome video series on LES/turbulence modeling. I learned so much, much more than following along with any textbook or college class- much appreciated! I would love to see future videos on the other sub grid models like dynamic Smagorinsky, one-equation kinetic energy model, etc. and a video that details the governing equations (Filtered Navier Stokes, Favre averaged equations) for explicit and implicit LES would extremely helpful!
@junjungarcia7236
@junjungarcia7236 3 жыл бұрын
great illustrations and explanation.....
@princeshapariya
@princeshapariya 4 жыл бұрын
Thank you Dr. Aidan Wimshurst.
@behzadlak5002
@behzadlak5002 Жыл бұрын
Perfect explanation!
@patelprem695
@patelprem695 4 жыл бұрын
You have great knowledge of CFD. I learn too many things from your channel but bit more curious and want to learn Explicit and Implicit solution scheme which is used in Ansys Fluent. Hope you will make a video on it. Thank you.
@armo66
@armo66 Жыл бұрын
absolutely brilliant!
@eslamredalotfy1985
@eslamredalotfy1985 6 ай бұрын
Very informative and full of LES clues, many thanks
@Martian2023
@Martian2023 5 ай бұрын
really like the style of your lecture
@hazemabolholl705
@hazemabolholl705 4 жыл бұрын
Think you for this great video. Now I start understanding the concept of LES
@yakovmosseri5818
@yakovmosseri5818 4 жыл бұрын
Very effective lecture
@cesaaargm
@cesaaargm 3 жыл бұрын
If any one of you has performed an IDDES simulation, I'd appreciate the exchange of thoughts and experiences about that topic. :D
@unverozkol
@unverozkol 4 жыл бұрын
Excellent explanation. Brilliant. Cheers.
@ricksaylor1953
@ricksaylor1953 3 жыл бұрын
Well done! Looking forward to more LES lectures.
@mdfaiazkhaled1347
@mdfaiazkhaled1347 4 жыл бұрын
Brilliant work. I wish you good luck.
@ankitranjan5696
@ankitranjan5696 8 ай бұрын
00:02 Introduction to Large Eddy Simulation (LES) 02:01 Turbulent flows have mean flow profiles with a range of eddies of different sizes and energies. 05:38 In Large Eddy Simulation, a subgrid scale model is used to simulate eddies smaller than the mesh resolution. 07:33 Estimating the optimal mesh size for Large Eddy Simulation (LES) 11:31 Large eddy simulation resolves only some eddies, not all. 13:30 A good Large Eddy Simulation resolves at least 80% of turbulent kinetic energy. 17:10 Understanding Integral Length Scale in Large Eddy Simulation 18:46 Integral length scale helps set up the mesh for LES. 22:11 Resolving turbulent kinetic energy using cell size estimation 23:55 Using the field 'f' to evaluate cell size for mesh refinement. 27:07 Introduction to Large Eddy Simulation (LES) Crafted by Merlin AI.
@MAHM0UDEMAM
@MAHM0UDEMAM 4 жыл бұрын
That’s a great discussion. Waiting for the next LES video.
@Mr.T-Drone-Pilot
@Mr.T-Drone-Pilot 4 жыл бұрын
Thank you very much. Can you do a vid on how the sub-grid scale is handled?
@fluidmechanics101
@fluidmechanics101 4 жыл бұрын
Yep, im planning on doing a few more in this series on LES. Stay tuned!
@abhishekbisht3897
@abhishekbisht3897 2 жыл бұрын
really lucid explanation . can you please upload some content on aeroacoustics as it also does need LES to solve the sound radiated by pressure fluctuation created by those eddies. it will be really helpful
@pawankumar-ir1fd
@pawankumar-ir1fd 2 жыл бұрын
Beautiful
@Yahyali-b6m
@Yahyali-b6m Жыл бұрын
thanks ver much. very wonderful course.
@CRONOSATOME
@CRONOSATOME Жыл бұрын
Very very useful and benefic!!!
@sanilgurung1356
@sanilgurung1356 2 жыл бұрын
made so much sense !!! thanks a lot
@helloworld4476
@helloworld4476 4 жыл бұрын
Great Video thank you very much! I would very appreciate if you make a video of using the LES for turbomachinery.
@fluidmechanics101
@fluidmechanics101 4 жыл бұрын
There are more LES videos on the way!
@markoj3512
@markoj3512 4 жыл бұрын
Hello Aidan, thank you for the concise explanation about LES. So if a fine proper RANS Simulation is done, a LES Solver with automatic mesh refinement would be very helpful generating a proper mesh for LES. But I'm not sure about the wall treatment in LES, because some RANS-Models use wall function other Models need a resolved boundary layers.
@fluidmechanics101
@fluidmechanics101 4 жыл бұрын
Dont worry, i am going to do a video on this soon. It is more difficult than you might expect because we want to keep the aspect ratio of the cells low, so the boundary layer meshes that we use in RANS arent good enough most of the time unless we use WMLES
@markoj3512
@markoj3512 4 жыл бұрын
@@fluidmechanics101 I will test your suggestion (5 cells across the integral length scale), but I'm afraid that the numbers of cell would increase dramatically. I remember that for a second order method in space, the numerical damping could be "neglected" if the length of a cell is about one order of magnitude smaller than the resolved size. So this would be an even higher restriction. Could you share your resource about the (5 cells across...)? Maybe I misunderstand something.
@fluidmechanics101
@fluidmechanics101 4 жыл бұрын
The recommendation of 5 is from an old ANSYS presentation. I will see if i can find a link for it
@faisalmohammad9383
@faisalmohammad9383 Жыл бұрын
Very well explained. Can u please also include the references for these equations and concepts? Thanks
@fluidmechanics101
@fluidmechanics101 Жыл бұрын
The explanation is my own take (so this video is the reference). For the equations, you could reference: S. Pope, 'Turbulent Flows', Cambridge University Press, 2000.
@faisalmohammad9383
@faisalmohammad9383 Жыл бұрын
@@fluidmechanics101 thanks a million
@chinthakaravinatha5230
@chinthakaravinatha5230 Жыл бұрын
Thanks, Aidan for the very insightful talk! As a good estimate for a finite volume scheme, it is mentioned that 5 cells across the integral length scale are likely to resolve 80% of the turbulent kinetic energy. How does this guideline translates into a spectral element scheme in which the higher-order polynomial functions are used to approximate solutions and these grid points are not equidistant?
@huixu7943
@huixu7943 4 жыл бұрын
Great video! Looking forward to the next episode!
@alimohammadigaragoz6057
@alimohammadigaragoz6057 Жыл бұрын
hi please make several videos about the Very Large Eddy Simulation Tanks
@jankracik1451
@jankracik1451 4 жыл бұрын
Hello Aidan, You did an amazing job! Thank you for all of us. Do you plan to make a video on differences between the Reynolds and Favre averaging? Thank you for your response.
@fluidmechanics101
@fluidmechanics101 4 жыл бұрын
I think i will do this when we start looking at compressible flow 👍
@RELBELE
@RELBELE 3 жыл бұрын
Super useful and very understandable! Great job!
@jloudefonty3231
@jloudefonty3231 2 жыл бұрын
Great session, thanks
@omidnazempour4954
@omidnazempour4954 3 жыл бұрын
very informative. Thanks a lot.
@BrandonLobo
@BrandonLobo 4 жыл бұрын
Very well done. Most sources do not really explain one of the core differences (TKE) between a RANS and LES, which is something you have covered. I currently work with LES for my dissertation and haven't really had the time to look into Hybrid RANS-LES. I know enough to include it in a literature review, but are they really helpful when compared to a regular RANS? I'm sure they are, else people would not use them, but why are they better? In case of external flows around a bluff body (airfoil, cylinder, automobile, etc) you are mainly interested in the boundary layer close to the body and a hybrid RANS-LES uses a RANS approach in these areas and LES around the RANS region as they are relatively a lot more expensive if you run a pure LES. The main reason to run a hybrid RANS-LES that comes to mind is the fact that the inflow profile would be more realistic, but I wonder if there are other reasons to it. Do you have any insight on this? More videos on LES would be awesome btw. EDIT: I'm guessing implicit vs explicit LES would be a good topic for a future video. I wonder if this is something your audience would be interested in. Implicit is pretty much what most people use from what I gather.
@fluidmechanics101
@fluidmechanics101 4 жыл бұрын
Yes everything you have said above is correct. Sometimes we care about the wake downstream of an object and it can be useful to have an LES wake even if the boundary layer uses a RANS treatment. Think about wind turbines. We would like to know how far downstream to place the next turbine. With a RANS model, the wake dissipates very quickly and it looks like you can place the turbines closer together. However the LES wake is less dissipative and persists much further downstream. Make you can add that into your literature review?
@BrandonLobo
@BrandonLobo 4 жыл бұрын
Haha... I should have thought of this because I'm working on wind turbine blade sections. Wind farm simulations in research groups that I know of use LES and discs in place of the turbine rotor. I'll find out if they use a hybrid method. It does make sense to use a hybrid method in cases like this thanks for that insight. I doubt they resolve the boundary layer in this situation for the cases I have in mind though.
@sauravpathak2116
@sauravpathak2116 4 жыл бұрын
As Versteeg mentions: there are two groups in turbulence modeling. 1. Make current RANS model more and more accuarate catered to a specific case, particularly for industrial application. 2. Search for general turbulence model (LES comes in here). Problem arises when we try to account for factors like anisotropy in turbulence. This is one of the motivation for developong LES too...cause smaller eddies are approximately isotropic. So, SGS can be used to model the effects of energy exchange. Well, some RANS model are designed to account for anisotropy but are not sufficient. And, the problem is: these model are more case specific. I have experienced this myself. As far as when we need LES as oppose to RANS, more specifically U-RANS. I would say, all cases 🤣 It can be deceiving when we see vortex shedding on a cylinder with U-RANS. But when lets say, we have a stepped cylnder- BOOM, U-RANS gives crap results. Sometimes, we dont even see mean flow variation in the wake. Edit: we can consider hybrid models. LES is certainly computationaly demanding. I usually prefer based on my aniticpation of how the flow field will look like? Massive separtion? Bye bye U-RANS.
@killua9369
@killua9369 4 жыл бұрын
Thank you for this amazing lecture! Which tool in paraview should be used to calculate the lo? Because I usually define a volField in the solver and compile it again
@fluidmechanics101
@fluidmechanics101 4 жыл бұрын
Just use the calculator in paraview. It should be fine. You will need to export the cell volume as a field from your CFD solver though 😊
@ardourmaker
@ardourmaker 3 жыл бұрын
Let me take a note here, thank you. 19:48 before run LES, a RANS simulation should be run to calculate l0 24:07 If f=l0/delta
@fluidmechanics101
@fluidmechanics101 3 жыл бұрын
Yep 👍 then once you have done the LES you need to check the TKE directly and remesh if necessary
@cfd2050
@cfd2050 Жыл бұрын
Great explanation!
@NitikaGarg
@NitikaGarg 2 жыл бұрын
Thanks for sharing very informative and intersting video about LES. Can you please share some information about monotonically integrated large eddy simulation(MILES) and how is it better than LES?
@arminsh9315
@arminsh9315 4 жыл бұрын
Thank you very much for your great videos. I am learning a lot from your magnificent channel and I am eagerly waiting for the next videos on LES. Also, I was wondering if you could make a video about functions we deal with in "fvSolution" like PCG, DIC, smoothSolver, symGaussSeidel and so on.
@fluidmechanics101
@fluidmechanics101 4 жыл бұрын
Yes these would make good videos and i might make them soon. You can always check out the book by Saad on iterative solvers for sparse linear systems in the meantime. Its really good for understanding the solvers and how they work 👍
@arminsh9315
@arminsh9315 4 жыл бұрын
@@fluidmechanics101 Thanks a million for your recommendation, I will surely start to read the book. I can't really wait to watch the video on this subject and also the ret of LES.
@mayuragrawal1060
@mayuragrawal1060 3 жыл бұрын
Very helpful video thanks Can you refer any textbook on turbulence?
@fluidmechanics101
@fluidmechanics101 3 жыл бұрын
Yep. 'Turbulent Flows' by S. Pope is a fantastic book for learning the basics of turbulence
@W0rtkarg
@W0rtkarg Жыл бұрын
Many thanks for the entire series! I still cannot figure out the difference between URANS and LES when it comes to the discretization of the underlying equations, especially the convective term of the NS. Is there any difference in the discretization of this term? Or is the only difference the way how we ad the "artificial" viscosity?
@fluidmechanics101
@fluidmechanics101 Жыл бұрын
You are correct. There is no difference in the discretisation! The only difference is the choice of interpolation scheme for the advection term. Upwind (1st order) is too diffusive. Many codes will insist on linear interpolation, or other second order accurate schemes
@skandasubramanya8707
@skandasubramanya8707 2 жыл бұрын
Amazing videos! I am addicted to your channel. Can you make a talk on hybrid turbulence models like DES, DDES and PANS?
@fluidmechanics101
@fluidmechanics101 2 жыл бұрын
Yep, they are planned for next year ☺️
@skandasubramanya8707
@skandasubramanya8707 2 жыл бұрын
@@fluidmechanics101 Oh boy! Will be on a lookout for those videos. Thank you.🙏🏼
@princevictorjenneyscharles8643
@princevictorjenneyscharles8643 4 жыл бұрын
Thank you, it is really useful and helpful. Pictorial presentation is really awesome. Expecting more videos from you. :-)
@mdfaiazkhaled1347
@mdfaiazkhaled1347 3 жыл бұрын
Brilliantly explained.. thank you so much...
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