In turbulence research validation by DNS is common, as far as I know.

I consider it to be a validation in stages: If the DNS code is valid, then the RANS model compared to it is valid as well.

I agree that in many cases, DNS could/should be more accurate than experiments, the major problem is of course that DNS data for high Re number are not probably available.  But if I could vote on "validation of a model" I say yes, let´s use DNS. I know what I am talking about -  experiments, I mean reliable and accurate experiments, are often difficult to obtain, mainly in geometrically complicated structures. And yet, to ensure correct and well defined boundary conditions - the problem that DNS does not have.  So what to do? Make for example Ercoftac community to raise a discussion? That is true that in many cases DNS is being used as a validation tool. 

The problem with validating models against DNS is that some or many of the DNS data sets have not gone through a proper scrutiny check themselves, see e.g. our assessment of available DNS data sets of one of the (not THE) most canonical flow cases, the zero pressure gradient turbulent boundary layer.

http://dx.doi.org/10.1017/S0022112010003113

However, ones such a scrutiny check has been performed (the details of which need to be discussed I presume), both DNS and experiments, should both be considered as "experiments", i.e. a numerical and a physical experiments, representing a "real flow case". As shown here,

http://link.springer.com/article/10.1007%2Fs00348-013-1547-x

it is not a validation against experiments, but a cross-validation of both sides.

The same as what has been mentioned by Dr Torsten Schenkel as well as Dr Miroslav Jicha, I'm agreed on validating the turbulence results using DNS. For instance, my results based on the RANS were completely in agreement with DNS and experimental results for turbulent boundary layer flows.

However, the only reason which can be mentioned for the tendency to compare RANS results with experiments is the limited Reynolds number which can be adopted for DNS due to the computational costs.

In P. G. Huang et all (2006), Compressible turbulent channel flows: DNS results and modelling, it is found that the DNS data do not support the strong Reynolds analogy.

http://journals.cambridge.org/action/displayAbstract?fromPage=online&aid=340249&fileId=S0022112095004599

DNS and experience are the references for validation of fluid mechanics turbulence models. the problem in DNS is that we refine the mesh to capture the too small cells in the too agitated zonnes. But it is very expensive in  point point of of view of comutational time and memory. An alternative is the "LES" which resolves large scale by a high-pass filter to the dimension of the mesh. this fitrage if dynamic gives excellent results. this approach is very good as compromise  "precision-computational cost and does not require solving other equations"; but it is transient. Another alternative is the K-eps or k-omega .... this approach is take few computational time but less accurate than the "DNS and LES", it asks the resolution of two additional equations for k and eps.

approximately. ideas

                  | DNS                | LES               | K-e

precision | 100%              |>90%             | 80-90%

cost           |  huge              |moderate      | low

hope clarifies the road and helps !

DNS is limited to low Reynolds number and simple geometries, but the validation of turbulent models needs to be done for a variety of flows. There exist a lot of experiment results and these can ensure a wider applicability of the turbulent model. However, DNS is good for analyzing mechanics of the turbulent models, to check whether the model item reflects the real physics, and to develop more physically sound turbulent models.

Well, it depends on the flow to be simulated. The computational grid required to do DNS for fully developed wall bounded turbulent flow is proportional to Re^2.75. Therefore, if the flow of interest is of low to moderate Reynolds number, it would be very appropriate to use DNS results for validation. However, a problem arises from the mismatch of DNS and RANS initial conditions. DNS of fully developed turbulent flow requires sepcfic initial conditions to generate turbulence in the system artificially without the need to wait for the actual physical time required for turbulence to develop. In RANS, this is not the case, since the Reynolds stress closure (eddy viscosity or Reynolds stress equations) dictates turbulence in the system by introducing the free stream turbulence intensity. In simple words: the alteration of these initial conditions play an effective role in matching both sets of results; RANS and DNS. 

If the flow of interest has high Reynolds number, it would be difficult to conduct DNS; unless there is a proper access to a supercomputer that serves this kind of simulations. This is not the case in the majority of institutions allover the world, especially in developed countries. Hence, experimental measurements are taken as benchmark to validate RANS simulations.

There's a very interesting issue regarding LES, which makes it an excellent alternative. According to Pope's famous 10 questions paper [1], as well as few other works [2,3], if the resolved turbulence kinetic energy of an LES simulation exceeds 80% of the total turbulence budget of the flow, the results can be considered somehow comparable to DNS results. Since the eddies with small frequencies transport the high energy spectrum of turbulence, one need a computational grid approximately proportional to Re^1.8 in LES to achieve this quality measure. And with the presence of a subgrid turbulence model, one do not need to introduce artificial turbulence to the system. Hence, and in my opinion, high-quality LES can serve as a validation benchmark for RANS instead of DNS in high Reynolds number and relatively complex flows.

[1] Stephen B Pope 2004 New J. Phys. 6 35 doi:10.1088/1367-2630/6/1/035

[2] Simon Gant Flow, Turbulence and Combustion, March 2010, Volume 84, Issue 2, pp 325-335

[3] Lars Davidson, 2009, Large Eddy Simulations: How to evaluate resolution, International Journal of Heat and Fluid Flow Volume 30, Issue 5, October 2009, Pages 1016–1025

Hi Heinz et alii,

validation of results is generally fundamentally difficult because in case of validation against measurements or observations there is the measurement methodology to be taken into account (device etc.). In the case that we validate against DNS we need to take the numerical method of the DNS approach into account.

Everybody here knows about spectral footprints of numerical schemes. If things are simple and we can idealize the problem under consideration then classical theoretical physics may help. I tried it with respect to neutral turbulence in an inviscid fluid (see attachment) where I found a.o. that von-Karman's constant is given by 1/sqrt(2*pi) ~ 0.399 (remember that the international standard value according to measurements and DNS is 0.40). Most real-world problems are more complex and need numerical simulations. But we should not give up only because of the non-linearities involved in Navier-Stokes. Molecular motions in a gas follow the non-linear Coulomb interactions, which are highly non-linear. Nevertheless, if many molecules are involved, we may use the "exact" classical gas laws. We talk here about the emergence of new laws. I would like to conclude that theoretical physics is still alive and possibly a nice supplement to the computing machine ...

In CFD tthe Reynolds number that you can solve for is limited because the computational requirements it asks to perorm a DNS is limited. The higher the Reynolds number, the smaller the smallest scales in a certain flow, the higher the resolution you need to cover the structures with spatial discretization points. The higher  the spatial resolution the smaller the time steps. Complex geometry (this starts already by having a wall) makes it even worse.

Hello

at present DNS is limitated by the computational power that is still not enough to solve high Reynolds number real problems. Nevertheless, DNS is largely used to test the statistics of LES formulations in specific and controlled test-cases.

I think that, due to many limitations in laboratory, experiments are also not a real problem assessment 

The validation with experiments is very limited because initial and boundary conditions are only known for limited parameters at limited locations at limited times with limited accuracy. So indeed, filtered solutions generated from filtered equations (either RANS and LES) can only be validated by DNS at limited Re number. However, you can use exactly the same  boundary and initial conditions by taking the appropriate filter over the exact ones! But do not forget to filter the DNS results when you compare them with the LES or RANS results!

Dear Heinz.

I will again express opinion of someone who gets to be Jurassic in science.

There are two problems in your reasoning, operational and other conceptual.

The operational problem is that the validation of simple cases as homogeneous fluids and other simplifying assumptions, validate a numerical model today seems something more than Jurassic my opinion.

You cannot and should not require the validation of a mathematical model using a physical model with the same boundary conditions and complexity of the flow of the simulated by numerical models. If this were the case would not be necessary numerical models!

On the other hand when the flow conditions assume more complex cases in which the same theoretical formulation not yet reached, validation becomes essential. A simple example is the study of medium or high concentration density currents with erosion and depositional (non-Newtonian flows with the apparent viscosity varying with the concentration).

As for the conceptual problem, of which I am not a big fan, is the circularity that is infringing when using the same set of equations with different methods, the DNS part of the same group of equations that any numerical method, and when we add the this simulation other variables and equations that's where the problem is.

Call validation of a mathematical model for other mathematical model is tremendously risky and reckless, because when this is done by inexperienced professionals will have a false confidence in the results that will lead in the future erroneous solutions. The technology is set up to work with people of average experience and not by experts in the subject!

I already have experience to verify that various mathematical models generate beautiful images, which unfortunately often has little to do with the physical reality of the problem, but unfortunately science will pay dearly for this, for many solutions that do not follow the trial will assign the error measures and not the model failure.

Standards such as ASME were created not for great researchers, but for ordinary people!

Sorry folks, I did a mistake forgot to attach the theory paper mentioned in my last comment. One of the results is von Karman's constant as 1/sqrt(2*pi) = 0.399, valid only for infinitely high Reynolds number. We all know that the international standard value is 0.40 and a recent study by Bailey et al. (2014) based on the Princeton superpipe gave 0.40+/-0.02. Here is the biblio data:

@article{baileyetal2014,

author="S. C. C. Bailey and M. Vallikivi and M. Hultmark and A. J. Smits",

title="Estimating the value of von {K}arman's constant in turbulent pipe flow",

journal="J. Fluid Mech.", year=2014, volume=749, pages="79 -- 98",

publisher="Cambridge University Press", doi="dx.doi.org/10.1017/jfm.2014.208"}

I mentioned in my last contribution that actually we cannot validate models against DNS due to the numerical errors (diffusivity etc.), that we cannot validate against measurements due to the measurement errors, and now I like to add that we also cannot validate against theory because mostly theory rests on abstractions, on ideal configurations like point masses, ideal lines, or inviscid fluids with Re = \infty. Conclusio: There is no help! But jokes aside: All means are helpful, in particular those which allow refutation of models by counterexamples so that the limits of models become clearer visibly.

Hello,

actually I do not agree that DNS can not be used as it is affected by numerical errors...

what happens is that the whatever numerical discretization is used, a local truncation error is produced. Nevertheless, If we talk of real DNS, the computational grid must be so fine that the action of the numerical error is practically zero since confined at scales lesser or comparable to the Kolmogorov one. If that does not happen and the numerical error acts at larger scales, we simply are not doing a DNS.

I think rather that the problem is in the fact that DNS  produces a (correct) solution but from a mathematical model that can be an approximation of the real physical one. Somehow, is this approximation we can not exactly control for a correct validation

Hi Fillippo,

the problem is that the question is posed too general. DNS, observation and theory, they all have their pros and cons and the devil sits in the detail. And much depends on the task to be solved. The TASK is the essence which determines what sort of methodology I should choose.

On the principle of independence of the boundary conditions of structure direction of turbulence

Lu Panming

Abstract

This is an introduction to the turbulence modeling theory of the present author, which can take the boundary conditions of turbulence structure into consideration ( the main contents have either not been published in normal journals or only published in chinese papers).   It is included that： (I)。Difficulty Problems Encountered in “Second-Moment-Closure” turbulence modelling ，i.e.  “Gao-Ge Anomaly” ;  (II)。The improvement  to the ”Second-Moment-Closure” turbulence modelling in order to allows the boundary conditions of turbulence structure direction could be prescribed;  (III)。An explanation to the principle of  independence  of  the boundary conditions of

turbulence structure direction ;  (IV)。Six suggestions to the possible future work directions;  (V)。 An explanation to the ”Gao-Ge Anomaly”.

------------------

4. The principle of the independence of the boundary conditions is not only to the turbulence modelling, but also suitable to the other subject, because it is frequently meet the equations are not easy to solve, so there is often a need of modelling or predigestion.  For example, both the D‘Alembert anomaly (~1752) and the Stokes anomaly (~1856), are due to breach the  principle of independence  of the boundary conditions, according to today`s point of view .This is because, first, by using the inviscid potential flow`s dynamic equations it is not possible to affiliate the slip-less condition of the real fluid at the wall, and  second, using the Stokes equation it is not possible to affiliate the boundary conditions both at the wall of cylinder and at the infinite to the cylinder.  The first anomaly lead to the discovery of the Prandlt`s boundary layer theory（1904）, and the  second anomaly  was solved by Oseen（1910）with introducing a modification. All these reflect the scientific worthiness and broad latency of the present principle   of the independence of the boundary conditions.

-----------------

above is an example paragraph,for more details or need the full text, please go to the end of this letter, where will be an web address existed.

http://staff.ustc.edu.cn/~pmlu/ 

Hello,

just to try to put alive this interesting discussion, I would post one of the state-of-the-art data-base of DNS cases.

http://turbulence.pha.jhu.edu/

They can be considered as real experimental ..

Turbulent flows through three approaches:

DNS computes a turbulent flow by directly solving the highly reliable Navier-Stokes equation without approximations. DNS resolves the whole range of spatial and temporal scales of the turbulence, from the smallest dissipative scales (Kolmogorov scales) to the integral scale, L (case characteristic length), which is associated with the motions containing most of the kinetic energy. As a result, DNS requires a very fine grid resolution to capture the smallest eddies in the turbulent flow.

https://engineering.purdue.edu/~yanchen/paper/2007-8.pdf

Dear Krishnan,

sorry but I don't understand the goal of your paper in this thread...

I have seen most of the turbulence models are being developed by comparing with LES data (Bardina, Ferziger and Reynolds 1983). 

Most widely used stress transport model ( SSG model ) is being developed and calibrated against direct simulation and LES data.

I think DNS data can be used for validating turbulence models.

For reference:

https://www.cambridge.org/core/journals/journal-of-fluid-mechanics/article/modelling-the-pressurestrain-correlation-of-turbulence-an-invariant-dynamical-systems-approach/3F54EAE2F2998E34ED7CC44D7048B73E

thank you for all your interesting answers,

consult this dear Heinz Herwig and good luck :

https://www.researchgate.net/post/Can_DNS_simulates_turbulent_flows

All this is interesting and the parties are all reasonably serious. However, what will we do with numerics when the kinematic (molecular) viscosity tends to become really zero like in superfluids? Asymptotics:

a) Empirically extrapolate towards the wall or,

b) come back to Kolmogorov and do a statistical theory, i.e. to a theory (i.e. a set of differential eqns.) for statistical EXPECTATIONS as state variables, as it is common in quantum theory? This approach is maybe more robust also for FINITE and SMALL viscosities sensu perturbing the state viscosity = 0.

Helmut Ziegfeld Baumert : Very thought provoking question. However, reminiscent of original idea behind Euler's equation, which was thankfully tackled by Prandtl's boundary layer theory. The essence is that in approaching a limit, we should not change the nature of the governing equation. Unfortunately, I am not knowledgeable in statistical mechanics, and hence cannot do much than expecting someone else to solve it! If statistical mechanics is the preferred tool!

When it comes to DNS, please also keep in perspective as to how we arrive at the governing equation. For example, I have my strong reservations on:

1) Stokes' hypothesis to be responsible for many ails of the governing equation.

2) Isotropy assumption of stress system. We need better constitutive equation including unsteady effects. Thankfully, these two aspects can be rectified in the realm of continuum mechanics, without dabbling in quantum mechanics.

These are my two pennies!

Tapan K. Sengupta: Sreenivasan mentioned on The Backpage of APS News June 2018 that not only continuum mechnics or statistical mechanics are needed to talk about turbulence. He mentioned even more fields of modern physics. They are called in Europe "synergetics" and headed by (a.o.) the teachers Hermann Haken (Erlangen) and Werner Ebeling (Berlin), see e.g. https://www.springer.com/de/book/9783540408246

My ref to quantum mechnics was meant initially in a methodical sense, as only ibe example that things are not so much exotic as they sound. But I just got papers about relations between quantum mechnics and turbulence.

This is of interest: when Kolmogorov's length scale becomes very short (very high energ flow like in Princeton's superpipe), it might become quantized, looses it's character as continuum variable. Remember Max Planck found out that the energy of elementary oscillators is quantized, no other explanation of the measurments! Well, and turbulence consists of vortices in interactions, cascades etc. These are already 3 cents!

Dear all,

how "very short" should be very short? :-)

The conflict of the Kolmogorov length scale towards the mean free path of the fluid?

In principle, we use the Euler equations as a mathematical simplified model but we disregard possible solutions that are mathematically but not physically admissible. And for such flow we assume no termination of energy cascade at the level of the Kolmogorov finite lenght.

I assume that the infinite cascade produced by the Euler solution is just a mathematical response, modelling the inertial energy transfer but not able to predict the dissipation. Similarily the NSE used for a flow that produces a Kolmogorov (but I would focus more on Taylor) lenght scale conflicting the limits of the continuum should be debated.

I think that a possible problem to be analysed should be focused on the assumptions such as Stokes and linear Newton closure. At the same time, the NSEs written over a finite lengt volume have different properties about regularity.

There are similar discussions on RG about alternative proposals.

@Filippo Maria Denaro is absolutely right. Let us explore all possibilities arising out of viscous flow description first, by exploring the remaining simplifications in Sotkes' hypothesis and in the model of constitutive relation between stress and strain. Lot of works need to be done there itself. We should not try to draw any conclusion on the solution of Navier-Stokes equation from the solution of Euler equation. These two are qualitatively different.

DNS can be used for validation but under very specific boundary conditions and some limitations and constrains. For some extend, the effect of turbulence on turbulent viscosity makes DNS is an inaccurate trend compared with experimental measurements.

Daniel Ahmed

not sure what do you mean: " the effect of turbulence on turbulent viscosity makes DNS is an inaccurate trend compared with experimental measurements "

In DNS there is no addition of turbulent viscosity. If the BC.s to be prescribed are the same of the experiment (a very very difficult task), you can be sure that DNS is much more accurate than any experimental measurement.

DNS is not capable to predict results accurately compared with experimental measurements ,in particular in high Reynolds number viscous flow(Reynolds number >4000) i mean that turbulent viscosity will be relevant. More work is needed to use turbulence model(RANS) related to practical applications.

@Ahmed Abdelhameed

Again DNS has NO turbulent viscosity as there is NO turbulence models in it.

If a DNS solution has problems they are due to a wrong use of the discretization and a wrong setting of the BCs. (I do not mention here the theoretical aspect of the validity of the NSE). But in no way an experimental measurement can reach the resolution of a correct DNS.

Agree completely with Filipppo! RANS and DNS are completely different levels of activities. Experiments still can't get us a good estimate of vorticity field. Thus, at best, experiments and DNS can be complimentary.

Thanks for all , DNS can be used for validation for laminar flow treatment what about turbulent flow where the effect of viscous term in Naveir stokes equation is relevant!!! however, in case of turbulent flow DNS may be used as a trend to validate the numerical results and very conditional experimental measurements

" DNS can be used for validation for laminar flow treatment what about turbulent flow where the effect of viscous term in Naveir stokes equation is relevant!!! "

Maybe you are not aware about what DNS means?

DNS is nothing but the numerical solution of the NSE on a grid so fine to resolve up to the Kolmogorov lenght and time scales. That means you can solve problems where laminar, transitional and turbulent regions can coexist! If a DNS solution would turn to be wrong (apart form lacks in the numerical setting) is because the NSE are no longer valid for that specific problem.

And yes, DNS is often used to validate the stitistical results coming from modelled simulations.

Kindly please, I am aware of DNS

A direct numerical simulation (DNS) is a simulation in computational fluid dynamics in which the Navier–Stokes equations are numerically solved without any turbulence model.

good, thus what your previously statement means?

I mentioned that you may use the predicted results based on DNS in order to validate experimental measurements from laminar flow regime. but in case of turbulent flow you may use turbulence modeling. But in case of using DNS to validate turbulence models that will be accepted as a trend in laminar flow of experimental conditions.

As per I know some group in Israel have done some DNS modelling of laminar flow only, still DNS in turbulent flow people have not done. I don't know whether I am right but once a scientist told us in a class.

Hello Santanu! There is no such thing as DNS of laminar flow! The people from Israel will not be excited by your revealation! There have been many claims of DNS for fully developed turbulent flows and these are in the published domain. So your scientist is not up-to-date, as some such work has started in 70's! We have taken the other route, where we start from receptivity stage to fully developed turbulent flow stage of a canonical flow. The DNS results post-processed show extremely good match with time-averaged experimental results. As you realize that with DNS results you get much more than time-averaged results.

Dear Sengupta sir, thank you for your writing. I will discuss this thing and I will post

It should be clear that DNS solves ALSO laminar regime. This is what happens at the scale of dissipation where the local Reynolds number is O(1) and at that scale the flow is laminar. The DNS grid has the step size comparable to that length scale that means the cell Reynolds number is also O(1).

@Filippo, for once I have to disagree with you. Of course for turbulent boundary layer over a plane surface without separation, one observes viscous sublayer where molecular diffusion dominates over eddy diffusion. One would be tempted to call this flow very very close to the surface of the plate as laminar, but the fluctuating component of velocity is small, but non-zero. Capturing this by explicit method restricts the time step for DNS to be overtly restrictive. However in LES the viscous sublayer is never resolved, yet in many reported solutions good match with experiments are known to have been shown.

Dear Tapan K. Sengupta

maybe I was misunderstood in my previous post. I denote "laminar" regions also in case of an unbounded flow (as in homogenous turbulence) that has 3D and unsteady fluctuations at the smallest lenght scale for which the corresponding Reynolds number is O(1). For me, the flow at the scales lesser than the Taylor microscale having no longer the inertial energy cascade, but following the dissipation rate, can be defined laminar at those high wavenumbers provided we see such fluctuations in terms of the congruent small lenght scale.

Dear Heinz Herwig, I would think that DNS is not really DIRECT. The numerical methods applied are ALWAYS connected with assumptions, as already mentioned by Lucky Tran years ago. Whether you use spectral, finite-difference or finite-element methods: it's all the same - a modification of the physics you wish to simulate.

I would suggest to use MD simulations to predict formulation or empirical formula of turbulent viscosity and you may use DNS to predict the characteristics of flow regime with no need to use turbulence models. I mean that MD simulations will give us the clue of viscosity leading to solve the mysterious of viscosity.

So you can apply DNS for cases of flow regimes providing the physics of viscosity is sorted out by MD simulations as a result you can use DNS to validate turbulence models for laminar and turbulent flow cases.

While I agree that any discretization method drives to the exact (in the sense of anaytical) solution of the modified partial differential equation, an equation that can introduce physical effects not present in the original one, any time we define DNS that means we use such a fine grid that any supplementary term in the modified equation are not relevant on the solution. Only in this sense we define a Direct Numerical Simulation.

To be more accurate, we can accept a small contribution of some numerical viscosity acting limited in the physical dissipative energy range but we cannot accept that numerical dispersion is a relevant action at such lenght scales

Dear folks,

validation of physical laws needs always to be specified as "validation with respeect to ..." - nature OR simplified laws known from school like Navier-Stokes. Howeber, what is NATURE in such a context? Yes, the result of measurements or observations, so we have always the technique of observation/measurement between nature and our brain and its abstract internal laws (Never forgotten: Newton took planets as point masses and succeeded; yes, we are living on a point mass ...). Applied to turbulence modelling this means at least that any DNS needs to be superior to any any observation/measurement etc.