(1). I have been thinking about this "DESIGN" definition for a long time. It started when I was working on the B-1B bomber in early 80's. (2). Now the bomber has been in service for many years, but I still run into this "DESIGN" definition puzzle. The question was " What is DESIGN?". (3). This was raised again recently, because a senior engineering specialist said,"He has asked the project manager to include the Navier-Stokes CFD analysis in the proposed new blade design." (4). So, before I was able to find the true definition of "DESIGN" , I am now facing another puzzle about the definition of "CFD Analysis". (5). A few years back, when I was wroking for a engine company (the name has just been changed),I remember that they used something like "Turbine Components Design and Analysis" for the department name (a large department with several hundred engineers). And, the Navier-Stokes analysis was included as part of the design sequence. (6). At one occasion, a manager made a statement that," his group is not using the Navier-Stokes codes in the design, they use only Denton's code. So, they don't run into the convergence problems associated with Navier-Stokes codes." So, I guess his definition of design does not include the Navier-Stokes analysis. So, this is different from the definition of the previous manager about the definition of design. (7). So, the puzzle is, "Is CFD Science or Art?" I hope it is not a religion.( I mean a company culture.) (8). The reason why this is very important is that, it will have a great impact on the future of CFD. (9). Before we start the discussion, I think, my definition of CFD is," CFD includes problem definition, complex 3-D geometry definition, the appropriate computational mesh, the turbulence modeling and the physical modeling, the numerical solution algorithms, the graphic presentation and animations, and the results interpretation." (10). I have shown ten years ago that these sub-elements of activities can be included in one single code for simple and well defined problem. So, there is no question about the feasibility of includeing the CFD analysis in the design cycle for the well defined simple 2-D problems. (11). So, the question can be refined further as " Is CFD Science or Art, for complex 2-D, 3-D problems ?" (12). Can we say that, the 3-D CAD can always produce the right geometry for CFD analysis? (13). Can we say that, there is a mesh generation code somewhere which always produces a working mesh? (14). Can we say that, we know enough about the turbulence modeling and by simple selection of a particular model we can always obtain a good solution? (15). What about the solution algorithm and the related boundary conditions, can we say that by using the highest order accurate scheme we can always obtain a converged solution? (16). Can we get any information easily anywhere from the flow field? Even for this seemingly straightforward question, I have been frustrated by the inability to locate the highly skewed meshes on the 2-D screen using some commercial codes. (17). Bill Gates is a great leader in the PC world, he also has a great heart. But it seems to me that the future of CFD requires a lot of work, far beyond the operating systems, word processors and spread sheets programs. (18). So, is CFD science of Art? That is a question in addition to my old puzzle, what is the definition of DESIGN?

Hi John,

The question can even be genralized to scientific computing in general. There is a famous book known as

Numerical Recipes or the Art of Scientific Computing.

The fact is that to write a code with all the initial conditions, boundary conditions, testing, etc... is to some extend an art, since one has to make a lot of trials and get the 'feeling' of how the code performs under certain conditions, even without the DESIGN and the rest.

So we have here a question of definition and classification. Personally I do not like to try to put stickers on things but rather just like to observe the world as it is. So I agree that CFD is not just science, but I would not say it is Art or something else.

Patrick

(1). 1+1=2, is (Math.) (2). F=m*a, Newton's second law (Science). (3). Navier-Stokes Equations, is Physics (Science). (4). Turbulence Modeling, is ? (Fuzzy Science). (5). Geometry modeling, is (Math.+ Art). (6). Mesh Generation, is (Math.+ Art). (7). Numerical Algorithm for CFD, is (Math.+ Art). (8). Visualization and Animation, is (Math.+Art). (9). Art is something unique,which can not be duplicated easily. Science is something universal, the theory is always valid. Math. is something reliable,which always produce the same answer. Fuzzy Science is something looks like science, but not yet qualified as universal. (10). By adding these together, the score for CFD is (Art-4, Math-4, and Science-2.5). The post-processor would be (Art-1, Math-1). The geometry and mesh generation would be (Art-2, Math-1).

You make my feeling for art more engineering than entertainment.

Turbulence modeling is Math!! All the theories about the spectra etc.. (Kolmogorov, and the rest) is not fuzzy science. There is a whole theory behind it, if you don't know about that then, maybe for you it is fuzzy, but certainly not for everybody. Chaos is a theory of theoretical physics and mathematics, and chaos is a natural solution of non-linear equations like NS. So NS and chaos looks chaotic to you, but there is a bunch of theories behind them. Geometry is Math too! Even its modling. If you want a good modeling then let a mathematician do the job... And, remember, turbulence is Universal, it is in the whole universe, at all scales (Galaxies, interstellar medium, intergalactic medium, etc..).

(1). I am talking about the "turbulence modeling". (2). The theory and mathematics of turbulence can only provide a series of equations which are not "closed", that is, there is no way to find the answer. (3). For CFD, we need to find the solution, and the "turbulence modeling" is the process to close the governing equations. That process is "Fuzzy Science", sometimes it works and sometines it doesn't. (3).I am not aware of a mathematician who works as a CAD engineer, a person who creates 3-D models using programs such as CATIA, PRO/ENGINEER, AUTOCAD, Microstation, CADDS, or 3-D studio, etc... I am talking about the final geometry model for the CFD , not the mathematical definitions of point, line, curve, surface. a CAD engineer (or designer) must have a very strong feeling about the 3-D objects.

i agree with you on all points but number (7) the development of modern CFD algorithms is math mixed with fuzzy science. it is true that older schemes were 'cooked up' but more modern techniques (TVD, DRP etc) have a solid mathematical base. when CFD schemes were based solely on the (nebulous) context of order of accuracy, which doesn't precisely mean much then you could say they were art but if we look at newer schemes the mathematical development is mostly rigorous. unfortunately most CFD users (or even developers) don't read Journal of Computational Physics etc so their appreciation of the strong physical and mathematical basis behind modern CFD schemes is lacking and so they are prone to think of these concepts as arbitrary

also i think the art in mesh generation can be removed (or at least reduced) by more wide use of techniques like adaptive meshing that take the subjectiveness out of mesh gen

As I see, the most TVD and DRP schemes are derived from the Euler equation. If one uses them for the NS equation, he is then uncertain whether these schemes are still available, because they produce numerical diffusion which can confuse the real physical diffusions such as viscous layer etc. In this sense, "solid mathematical base" is restricted. I hope you would give a comment.

X. Ye

(1). I think you are right. I was not trying to find a middle ground to present it so that everyone can accept it. (2). There is a very interesting paper on "Accuracy of Shock Capturing in Two Spatial Dimensions" by Mark Carpenter from NASA Langley Center, in AIAA Journal,Vol37,No.9,September 1999. In the conclusion, he asid," Results show, contrary to conventional wisdom, that captured 2-D shocks are asymptotically first order, regardless of the design accuracy of the numerical method that is used to obtain them." In showing this results, he has used a linear fourth-order method and a nonlinear third-order method in the study. (3). In other words, it is not possible to capture something which is smaller than the cell size, regardless of the order of accuracy of the method used. (4). One more thing I didn't mention in the message was, the trend to more user-friendly graphic user interface and interactive environment is the trend to more art approach. In the robotic IC assembly line, everything is pre-programmed event. I don't think that the current trend of CFD is heading in that direction.(it would be very efficient to get thing done that way, if possible.)

DRP (dispersion relation preserving) schemes have nothing to do with artificial viscosity they are schemes which allow for the capturing of high wavenumber disturbances with minimum grid points (read Tam and Webb's paper in J comp Phys, 1993 i think). these schemes were developed for Aeroacoustic analyses and they allow for coarser meshes and when combined with an optimised time stepping scheme (Hu et al J Comp Phys 124 pp 177-191) allow for larger time steps as well. these schemes and others similar have been derived specially for Comp Aero Acoustics (CAA) but can be used for CFD and give the same benefits. if you read the papers you'll see that the numerical schemes, the stability limits and more important the accuracy limits are defined quite rigorously. such rigor is characteristic of CAA schemes (and articles published in J. Comp Phys.)

one of the points i mentioned before is that some journals like J. Comp Phys., and SIAM journals, and applied math journals often contain the derivations of the numerical schemes that we use. however many CFD users don't bother to read these they tend to stick to the 'applied' journals hence missing 'details that are presented elsewhere' in doing so they ignore the rigor and get the impression that these scheme were pulled out of someones ass (to use the colloquialism)

as a result we have lots of users (and developers) going around saying i'm using Jameson's scheme or van Albada's limiter (etc) and having a poor understanding of the advantages and drawbacks of the pparticular scheme they're using. yet in most cases comparisons and developments of these methods are available in the 'rigorous' journals but many don't read them because they are 'full of math'. it is the bane of many engineers that so many of us seek to avoid the details of mathematics whenever we can. but God is in the details. many of us wonder why our codes don't work as well as the papers indicate they should but don't have a deep mathematical understanding of what we're doing the we get mad and say CFD is bullshit and don't get anything done.

Thanks for your comment. Really, for an enginner it is not easy to understand the mathematics behind the numerical schemes. But on the other side, the theorists should consider that the engineers are confronted every day with practical problems governed by the NS equation, hence they should derive and test their schemes for NS euqtion. Maybe, the DRP schemes are very good, but could you mention a paper in which the author tests his scheme for NS equation, for flow with boundary layer? Is the artificial viscosity the unique reason for the numerical diffusion? I am not sure. It seems that the theorists avoid always to touch the complexities of the NS euqtion and let the enigeers use CFD as an art. It's a pity and I am not satisfied with this situation.

X. Ye

For theorists, CFD is science, because they treat the problems on a strict mathematical base. But for convenience, they avoid always to face the complexities of practical problems governed by the NS equations, derive and test their numerical methods for simpler cases governed by Euler euqation. Then they let the design engineers to have a grey zone to use CFD as art in treating practical problems governed by NS equation. The life is easy for the theorists but is difficult for the engineers. I think, it is the resposiblity of theorists to touch the complexities of NS equation and to invent generally available numerical methods, so that the engeneers can use CFD not as art but as science.

X. Ye

I'm using John's numbering system again

(1)i'd say your characterisation of the papers i was talking about as being written by 'theorists' is too general while it true that many of these persons (Tam for example) are applied mathematicians we shouldn't cast the nonengineer aspersion on them (they can't help it). you'll find that the people writing these papers are all the people you've heard about in the past as being originators of the schemes we use everyday (Roe, Jameson, van Leer, Patankar, Thompson etc).

(2)the mathematics used in these papers is not terribly advanced. i'm a second year master's student and for the most part the math is not beyond me. mostly your see series expansions and transforms (laplace,fourier etc) that we should be familiar with. maybe you'd not want to replicate the manipulations (why should you) but you can understand from reading them what is going on. so in general i would not say these papers are beyond the math abilities of most CFDers.

(3)in particular the DRP schemes were specially developed for solving CAA problems where the linearised euler equations or the full euler equations are used. however Tam ( J. Comp. phy. 1993) indicated that versions of them could be derived for the NS equations as well. in fact Dr. Philip Morris here at Penn State has used a DRP scheme to solve the (so called) Non linear disturbance equations which are a perturbation form of the NS eqtns. his email is pjm@psu.edu nd i'm certain he can give you the relevant references.

(4) this DRP scheme is for CAA so you may not be too interested however i must say that reading theoretical journals like J. Comp Phys, or J Fluid Mech etc is good because these are where the new schemes and their derivations are presented. the quality of submissions is very high and the characteristics and motivation for the methods are clearly and explicitly laid out, unlike in the 'applied' journals where such descriptions are glossed over. Case in point: no doubt you've read Jameson, schmidt, and Turkel's famous 1981 paper on the first application of the four stage runge kutta scheme with art. vis. for the euler equations. if you read the references though you'll see that Jameson had published a paper earlier where he develops the scheme. no doubt this paper gives the in depth motivation etc for the scheme. now this scheme is probably the world's most popular for solvinf CFD problems yet most of us have not read the original development.

(5)you speak of the NS equations. i think the main difficulty in solving the navier stokes equations in the industrial (applied) setting where turbulence is the rule centers on turbulence modelling. earlier in this thread mr Patrick Godon (who i think is a physicist) said that the theory of turbulence (Kolmogorov etc) is firmly based and i do not disagree. but engineers need to evaluate and here is where the fuzzy science (as John said) of turbulence modeling kicks in. it seems strange to me for example that persons would use the k-e model, which was developed for high Re external flows where viscous effects are limited to shear regions (ie aircraft aerodynamics), to problems involving internal flow of fluids at lowere Re where the flow is fully developed (ie turbulence is every where in the flow). i don't know much about turbulence as i'm taking that class now but i think that is our greatest problem in CFD

I'll try exclude the problems of physics such as turbulence modelling etc. I'll focus on the numerical method. I can describe the poor situation in terms of numerical schemes through a very funny example that I heard from a young professor of the University Düsseldorf: There was once a benchmarking case in Germany, namely the von Karman's vortex street under the Reynolds number of 100. The physics in this case is very simple because it is a purely laminar flow. Numerous universities and research institutions in Germany participated this benchmarking, but none of them could simulated this flow correctly because their numerical schemes were not fully available for this case with viscous layer and governed by the Navier-Stokes equations. From this example, one obtains the impression that the distance between the development of the new numerical schemes and the practical application in the industry is still large. Maybe in some years this leakage will be filled.

X. Ye

It is good to know there are people like mathematics and physics in the engineering world! It is very important to know the theory behind every engineering methods (CFD is one example), but it does not need to worship math. and physics.

To explain my point, let's go back one step to an even simpler question: How do we know the world? If you don't know the answer, you may get a clue from your academic degree. BS., MS. and Ph.D.. The first two are easy to understand: something to do with Science (even we are working on engineering, we got Science degree). The third seems odd, how come we got a degree in Philosophy. Well, that is the way that science starts with.

The word 'Science' was from Greek, which means 'I know'. The word 'Philosophy' was also from Greek means 'I think'. The world and everything within are 'facts' which exist before we 'think' or 'know' it. We must 'think' it first before we can 'know' it. For example, human knowledge starts from Philosophy (ideas, thoughts, imagination, etc.), then the Philosophy needs to be proved true by means of scientific (already proved to be true - 'known') process (like observation, measurements, etc.), then it becomes a new subject of Science. Next people want to understand it so they set up a model to describe it by menas of a series of symbols and relations (Math.) and then find use of it (Engineering). At this point, everyone made contributions got credit of 'invention, or discovery, or something'. After that, it becomes a common knowledge and we can learn it from books. Then we start to argue if it's right or wrong. Think the approach: Facts - ideas - models - apply to facts. which one is more important? Different people have different answers: physicis says ideas are more important, no ideas, no sciences; mathematics says models are more important, no models, no understant; engieering says application to fact is more important, it starts with fact and end with fact, all others are 'tools'.

Take TVD scheme for example, the concept was derived from the mathematic property of hyperbolic equations regardless its physical meaning. The TV (total variation - a human defined term) will not increase as time goes on, in another word, it will be D (diminishing). This is a Math. property of monotonicity. The 'Philosopy' behind the TVD numerical scheme was that if a numerical scheme preseves TVD, it will prevent 'over-shooting' near the discontinuities (like shock waves, etc.). Then there is a rigorous derivations for a large family of TVD schemes (math.), then there are applications of the scheme to engineering problems (CFD is one of them). Do you what is the real problem? the mathematical theory of TVD is known only to scaler non-linear hyperbolic equation, or linear hyperbolic system equations! It is unknown for muliti-dimension, non-linear system equations like Euer/N-S eqs. Do you still think TVD in N-S eqs. is a rigorous science?

How about turbulent model? Does anyone have a clear 'idea' what tubulent is? If there is no valid 'philosopy' model, how can one develop a 'math.' model?, if no valid math model, how can one say it is a rigorously developed science? On the other hand, is the Reynolds averaged N-S equation a correct approcah to the physics (fact)?

(1). Even though I try to use the words "science" and "art" in the over-simplified question, there are good reasons behind it. (2). The question of " Is CFD Science or Art?" is itself a valid question. (3). The question of " Who is doing what " is another issue, which is also very important to CFD as a whole. (4). At least at this point, there are "CFD engineers" and "CFD theorists" in the CFD field. (5). The CFD theorists are professors working in the academic institutions, where one of the major goal is to develop new theories or technologies and publish the technical papers, without the pressure from the project deadline. (6). Then there are CFD engineers who are responsible for brining the CFD answers to the design described in the project plans. (7). In this case, I think, somewhere along the line, there is something missing between the papers published by the CFD professors and the CFD engineers. So, what is missing? (8). I don't know exactly what is missing, but, I think it has something to do with the "Design". In other words, both sides were not able to connect their activities in CFD to the definition of "Design". (9). By definition, design must be carried out iteratively and in the process, the configuration (the geometry) must be changed many times. (10). When a CFD professor developed a shock capturing method and demonstrated the results in one dimensional flow, the method is good for the one dimensional flows. When someone incorporates the method in a 3-D code, the geometry will be very different from the original one dimensional theory. The users will likely run into troubles, because this CFD design (the change in geometry) is outside the original range of theory. But, if the users keep within the original scope of the 1-D theory (the 1-D design limit), then he is likely to get the right answer. (11). The code validation is actually a very backward method,because it is trying to figure out the applicable range of design. (12). My feeling is, if both CFD professor and the CFD engineer ignore the importance of the CFD design issue, then the CFD technology developed is no longer applicable in the design processes. Even though one could still have a paper published and a code used.

i understand your example. this case is simple in a way since turbulence modeling or compressible effects are not relevant. at the same time the problem is (extremely) unsteady and requires very fine mesh in the regions of the vortex separation from the cylinder. also the problem must have a clean spatial differencing scheme because the flow is affected by numerical dispersion.

however i have seen solutions to this and similar problems. one was a Finite element solution i saw in journal way back. i've also seen a solution (a video actually) using adaptive (cartesian i think) meshes by Pratt&whitney/united technologies research center. also i've seen unsteady solutions of axial and radial turbomachinery which resolve vortex shedding phenomena in a compressible flow (nice huh). you can see these in one of the VKI's lecture series notes on turbomachinery CFD. i could probably find the reference if you're interested.

i think for the anecdote you cited what happened was the researchers all had time marching codes set up for steady state analysis. and while in principle it is easy to do both steady analysis and unsteady analysis with the same code. in practice if the code is written from the start for steady analysis the unsteady capabilities are often compromised

on point (3) i fully agree. this is the essence of discretization methods. i've only seen a couple papers where the internal structure of the shock is investigated and both were very interesting.i also agree with your point (4) if we look at the computational structures field, all the cutting edge research is going toward automatic optimisation and automatic design i.e. less interactivity. they took the user of analysis a long time ago with automatic meshing and mesh adaptivity and we here in CFD are stuck with elliptic mesh generators. in CSM i think there is more pressure from the top (research) and bottom (users) to adopt cutting edge techniques in everyday work as they are introduced and validated (well the validation is easier so that helps) butin CFD we like to hold on to old things. in FEM nobody uses direct solvers anymore it's all wavefront solvers or advanced sparse matrix techniques, but in CFD we still have people using maccormack when MacCormack himself probably doesn't use it anymore. i've even seen Papers of Jameson's where he doesn't use his famous 4 step RK scheme (it's an oldie but goodie though). Some readers of my psots may dislike my harping on the CSM field over CFD but those of us who strive for excellence should emulate the sucessful traits of the more advanced

"DESIGN OPTIMIZATION" of the product visualizing the CFD simulation output. This is how to bridge the missing gap between design and CFD simulation.

(1). Yes, it is something like that. (2). But if we try to implement it as the creation of "CFD Design Optimization Engineer" to bring the two activities together, I don't know whether it is going to work. (3). For example, as a result of hurricane Floyd, many places in North Carolina are flooded and houses under water. To solve that problem, I think, pumping stations can be created and waterways built to transport the excess water . But right now, you can't just put a lot of water pumps in the flooded areas to start pumping water. (4). On the other hands, the earthquakes of equal strength hit both Turkey last month and Taiwan this week, but the degrees of damage are different. This was reported to be due to the building codes used in Taiwan. (5). So, I think, to make the "CFD Design Optimization" work, it must be incorporated in the method development phase, as well as the design application phase. (6). If the "CFD professor" (the person who develop methods) can demonstrate that the method can always provide a consistent results through "Design Optimization", then, there is a much bigger chance for the code to produce useful solutions later. This is a relatively new concept, even though it has been done through the use of grid independent solution exercise. This is because once the mesh independent solution is established, the users can optimize the design using the optimum mesh and arrangement. For example, if a 200x200 mesh has been demonstrated to provide mesh independent answer, then the user can weight his mesh size and the solution accuracy to arrive at the best solution in the actual design applications and still be able to get acceptable answer. (7). But, this is only a very small factor in the Design Optimization. How to incorporate the Design Optimization concept at the stage of method development is a wide open issue, something like the building codes used in the Taiwan's earthquake resistant building design. It is probably hard to make a conventional building earthquake safe after it is build. I guess, the same is true for a CFD method. If someone can come up with a mehtod which will solve your yet undefined CFD problems ahead of time, he must have the quality like Albert Einstein. For the rest of us, we must somehow look at the DESIGN issues before the methods are developed and after the application projects are prepared.