Hi,

There have recently been a few interesting exchanges on the list regrarding CFD market size and its potential growth.

I am curious as to how much of the market is 2D related.

Is there commercial interest in solving 2D problems, especially if one can do a successful 2D DNS (no turbulence modeling) of complex geometries for Reynolds numbers of say up to 50,000 (which is already too high considering that 3D effects kick in much earlier)?

Thanks in advance for your comments

Adrin Gharakhani

From the user's point of view (the user of a commerical code), he is interested in solving the real world problem. The assumption behind using a commerical code is to save time ( the time required to develop his own code). Unfortunately, the real world problem is highly 3-D. Even with a commerical code, it can be very time consuming to build the 3-D model and to obtain the 3-D solution. (sometimes, it takes several weeks on workstation for a run ). Sometimes, you are limited by the computer memory ( a workstation with one giga RAM is needed for 3-D un-structured mesh problem using a commercial code ). With these two limitations ( time and memory), users frequently are forced to solve 2-D problem ( model problem ). I would say, most real world 3-D problems are still un-solved because of computer speed and memory. The design procedure being used today is still: 1-D analysis, 2-D analysis and 3-D analysis. 2-D analysis is still part of the design process. The actual need for commercial code is in the area of 3-D complex geometry flow problem, where the need is not high enough to justify the in-house code development. The design code, 2-D or 3-D, normally are generated in-house or highly modified in-house. So, the 3-D world or the market is still wide open. ( because researchers are still trying to solve 2-D problems ). In short, users need 3-D solutions, but they are forced to solve 2-D model problem because of computer speed and memory limitations. The market is still 3-D. There is no 2-D airplanes, cars, and ships.

>Even with a commerical code, it can be very time consuming to build the 3-D model and to obtain the 3-D solution. (sometimes, it takes several weeks on workstation for a run ). Sometimes, you are limited by the computer memory ( a workstation with one giga RAM is needed for 3-D un-structured mesh problem using a commercial code ).

Well that depends.... If you want engineering answers on industrial timescales (where time to market is counted in weeks and design optimisation in days) then there are commercial CFD codes (sorry, codes that employ CFD) that fulfil that role. I have modelled large telecommunication rack systems with a structured cartesian grid using 100,000s of cells that take a day to build, an hour to grid and I have my convergged solution ready for me when I come in the next day. I can guage wether the current design is thermally efficient and if not can investigate a number of design variations within a week. This form of CFD analysis comprises the other % noted by Ferit.

Maybe people are heading in the wrong direction of using un-structured mesh ( which requires large computer memory ), or maybe we simply don't know what we are doing. I am sure that structured Cartesian mesh requires less memory, less computing effort. But the capability to handle the complex geometry is not as good as un-structured mesh approach. You have just pointed out a very important direction : " Quick 3-D answer with useful results " , that is 3-D PC games approach ( vs 3-D movie quality pre-rendered animation, which is slow ). This is probably a more attractive market, that is a fast 3-D code which will provide 1st order useful solution for engineering application. Just like the computer animation field, you have game-quality ( 3-D real time) vs movie-quality ( 3-D ray-tracing ). Thank you for your information. This market maybe more profitable. As a matter of fact, you really don't need the exact 3-D answer. What you need is something to guide you to a better design. This will definitely change the balance of the CFD market place. ( the need of user for a quick and useful 3-D CFD answer ). Thank you again for your information.

To answer Adrin's Q: A lot of CFD work in the real-world marketplace is 2D. By "a lot", I mean about 50-60% and this number will depend upon which sub-field of mech/chem/materials engrg you are talking about. The reason is that even though the problems may be 3D, quite a bit of qualitative information can be obtained from 2D analysis, and in fact is routinely obtained. A number of times, with a few simplifications to the geometry, 3D cases can be solved with the 2D axisymmetric assumption. The auto industry I'm familiar w/ certainly is an example.

Thanks for an interesting exchange! I have no doubt that the real world is 3D (actually it is 4D, I never liked "steady state" solutions - alot of significant information is lost by this assumption, but I digress).

The reason I asked about the 2D market is precisely because 3D codes for complex geometries (unstructured mesh) are practically out of reach for many engineers unless they have their hands on massively parallel or supercomputers. On the other hand, the very fast structured finite-difference solutions are limited to simple geometries (this is not entirely true, though!). So, I assumed that many would be "forced" to solve 2D model problems, but the question is how many would be willing to pay for a code like that. (I don't know, do the current commercial codes offer their 2D solvers as a subset of the 3D, so that users don't have to get separate codes?)

OK, now that we "agree" that ideally we need 3D solvers but for now we can afford "only" 2D, the question is "how important is it that _that_ 2D solution is obtained accurately and without turbulence models?" (this means a solution with least (or no) amount of empirical data manipulation, and very little numerical diffusion which finite-volume methods suffer from). Does the average user care at all to get an accurate solution to an already watered down 2D model?

Thanks

Adrin

I think it is easier to answer your question in this way: take the turbine engine components design and analysis in industries for example, in the design and analysis loop, you have to do 1-D analysis, 2-D axisymmetrical analysis, 2-D inviscid or viscous analysis, 3-D inviscid analysis, 3-D viscous analysis, ( and /or 3-D multi-stage transient analysis). A typical 1-D run takes one second. A typical 3-D run using structured code takes 15 hours. This is for the simple well-defined blade geometry only. ( mesh is always automatic ). Problems other than this have to be defined individually. In other word, 2-D and 3-D, inviscid and viscous analyses ( or codes ) are being carried out on routine basis. The market for these codes are always there. As for the commercial codes, some provide a 2-D option ( code) so you don't have to run 3-D code for 2-D problem. In the 3-D ( or 4-D) real world, are engineers running 1-D codes ? The answer is YES. Are they running 2-D codes ? The answer is YES. Are they running inviscid codes? The answer is also YES. At each stage, they extract unique information from the analysis. But the real need to do analysis is for " competition" in the product market. If you can come up with a better product by just using 2-D analysis, you are free to do so. ( something like the secret formula of Coke ). It's hard to make a living by creating a secret formula.

I don't see a lot of fluid dynamics applications where there is a need for more accurate 2D laminar solvers than those we have available today. Perhaps some special cases where laminar separation is critical could warrant a special "super accurate" 2D code, I don't know.

Most 3D codes offer the possibility to run 2D cases by just using "one layer" in the third direction, or something similar. It isn't as fast as a dedicated 2D code of course.

You said something about "2D DNS" in your first post. This might be self evident for you but just to avoid any missunderstandings - to capture any turbulent effects without using a turbulence model you must run full 3D instationary - there is no such thing as 2D turbulence (at least not generally speaking, although you sometime can see that term used in geophysical applications).

Just my $0.02

There is always a great need for fast and accurate numerical algorithms for solving Euler or Navier-Stokes equations. The laminar flow is ideal for such method development because you don't have to worry about the effect of turbulence modeling. so you can focus on the method development. The methods available for solving the Euler equations or Navier-Stokes equations are too slow, and the convergent characteristics unreliable. Even though 2-D methods sometimes can not be fully utilized in 3-D problems ( the difference between 2-D and 3-D is not equal to 1-D ), it is the starting point for method development. If you can come up with a method which will reduce the computing time by 50% , the productivity is easily a factor of two. ( you don't need a super-computer to work in this area to develop a fast and/or accurate method). Todays methods for compressible flows calculation ( with or without shocks, low speed or hypersonic ) are "FAR FROM IDEAL". In the design loop, you definitely would like to have the results back in 8 hours ( one day ) or less. Thirty minuites to one hour would be ideal. That's why 3-D Euler codes are still commonly being used in the design loop ( less than 30 minuites a run). There are four areas which require special effort: 1),complex geometry ( realistic geometry ) and mesh generation ( consistent with solutions), 2),fast and accurate solution algorithms ( and reliable too), 3), turbulence modeling ( any level, algebraic, 1-equation, 2-equation etc. , accurate wall parameter prediction: skin friction and heat transfer ), 4), integrated graphic and animation CFD codes ( check-out the intermediate results, and control the solution parameters easily without going back-and-forth between various codes). The starting point is the 2-D where the hardware and the programming software are widely available. ( If you can cut the computing time of Euler solution from 30 minuites to one minuite, you have achieve the productivity of 30 times. I think, it's highly possible that someone will be able to do it. ) The CFD-war is not over, it has not started yet!!!

> there is no such thing as
> 2D turbulence (at least not generally speaking, although
> you sometime can see that term used in geophysical
> applications).

Hey, there is such a thing as 2D-turbulence Sure it's not 'turbulence' in the conventional sense, but it still exists. I prefer to call it chaotic flow, a consequence of bifurcations in solutions to the 2D Navier-Stokes equations.

The reverse-energy cascade in 2D flows is an interesting subject in its own right, but I agree that it's not always relevant to engineering flows. However, it is valuable in understanding of how fluids can behave in the absence of 3D effects. If you don't understand 2D fully, then 3D is REALLY hard!

I would regard 2D DNS as calculating fully-resolved, time-dependent solutions of the 2D Navier-Stokes equations. Of course, this is different to DNS in the usual sense (ie: 3D N-S), but it is still direct numerical solution of the governing equations, albeit in 2D.

I believe the question is whether 2D calculations WITHOUT turbulence modelling is industrially relevant. As you say, where laminar separation is crucial a high-accuracy 2D solver would be critical. What proportion of 'engineering flows' lie in this category, I would suspect that many do.

Thanks for listening

Kenji Takeda

High Performance Computing Centre

University of Southampton, UK

I agree, but just to make it even clearer - the 2D DNS you refer to (fully-resolved time-dependent solutions of the 2D Navier-Stokes equations) has no relation to a real turbulent flow, even if the mean flow is 2 dimensional!

Turbulence in real life will always be 3D instationary.

I haven't been keeping up w/ the discussion but, I'd like to point out that a number of commercial software offer the choice of running 2-D or 3-D models. And a lot of unstructured codes are doing very well...Fluent, Star-CD, CFD-ACE+...codes which are very accessible to the user, and cost a few thousand dollars.

I think there's a distinction between a true 2D code and a commerical code that solves in 3D but with just one grid cell in the 3rd dimension (and symmetry boundaries either side). Is there?

An interesting breakdown would be the proportion of 2D simulations in the CFD software application area classifications highlighted by Jonas. I imagine in an industrial setting the % 2D simulations would be of the order of 5% for most applications. In academia this would certainly be higher. Hey, since when has academia been interested in the real world

It is very important to know that market can be created at any time. The product itself does not have to be very good in order to be accepted by the users. So it depends on how you introduce the product to the users ( or the market, if it is already there). It can also be done from the legal side by setting the requirement to use a 2-D code before a license is granted. In the 2-D world, at least you don't have to worry about whether users have a super-computer or not. And this is very important. I must say that, the 2-D market is still waiting to be created by someone who knows how to introduce a product to the users. Millions of people whould be very happy to use the code if they can derive " something " from using it. That " something " ( unique features ) will be the key to the market. So somehow you need to identify these features in additions to the creation of the 2-D code itself. In terms of users equipment, the 2-D market is un-limited while the 3-D market is limited. Whether the solution of the 2-D code is in any way related to the real world problem is not essential to the " 2-D market " issue at all. Unless that is your purpose of selling the code. ( Some users may want to display the code on that wall just because it has excellant graphic design.)

>I think there's a distinction between a true 2D code and a commerical code that solves in 3D but with just
>one grid cell in the 3rd dimension (and symmetry boundaries either side). Is there?

I don't think so. But if there is, I'd like to know what it is. My understanding is that there is no real cell in the 3rd dimension. That is only a manner of speaking. "Unit thickness" again is only a manner of speaking. The seven-point stencil basically gets reduced to the five-point stencil when you choose the 2-D option.