Dear All,

I have two questions:

(1) Is DNS the final solution of turbulent flow ?

If yes, can we say that turbulent flow problem is theoretically solved ? What we need to do is waiting until the computer power is good enough. Therefore, what we are doing (RANS or LES) is theoretically meaningless.

(2) As we know, the artificial viscosity is needed when using Jameson's central different scheme. But why it seems not appeared in SIMPLE method with central difference scheme ?

Regards

Li Yang

(1) Yes, since DNS doesn't need any empiricism. In fact it is not the final solution, it is not a solution at all : it just consists in solving exactly NS equations - avoiding also numerical artifacts ...

From Spalart (1999) point of view, the used of DNS for industrial cases won't append before 2080 since it needs 10^16 grid points and 10^7.7 time steps.

So turbulence modelling (RANS, VLES, LES) still have their interest.

sylvain,

Could you please explain why DNS is not a solution of turbulent flow at all? Is there any better numerical solution than that from DNS ?

Regards

Li

DNS solves the Navier-Stokes equations without any approximations, but Navier-Sokes is just a model and not reality.

What then is the cutting edge mathmatical description to Fluid Flow ? We have the Navier Stokes equations, but is there something more toical or cutting edge ? What other methods are there ? (Discreete Vortex methods ?) Bob

The NS equations are a simplification of the Boltzmann equations, and as such represent a "simplified" model of physical reality.

Well put, sometimes this is forgotten, and in fact in a series expansion of the Boltzmann equation the NS equations (in fact the momentum equations, since that is what the NS equations should actually refer to) represent the first term in this series,

Just my 2 pence worth

Andy

The first question was whether turbulence is indeed described by NSE. This is not trivial. If you add a small amount of polymer the viscosity changes only a little, but, say, in a pipe flow the pressure gradient changes considerably for the same flow rate. This cannot be described by NSE. Twenty or thirty years ago there was a lot of research into it. Finally it was found that small amount of polymer makes the fluid strongly non-Newtonian without significant change in viscosity as measured by a viscosimeter. Sorry, I cannot give references, long time no see, but one of the key names was Ioselevich, I think. Now it is generally accepted that turbulence is just a feature of NSE solutions.

Then, what is the problem of turbulence? It is formulated in the following way:

To calculate the averaged characteristics of interest without calculating the entire instantaneous velocity field thus saving computing time.

After all, if we want to know less, we may hope to pay less.

Therefore, the problem of turbulence is not solved yet. DNS does not solve the problem since it calculates everything. RANS, LES, etc. represent attempts to solve the problem of turbulence, and they are partially successful.

In more practical sense, if the computer will be strong enough to calculate the pipe flow at Re=10**7, we may always want it for Re=10**8, and for entire aircraft, not only a pipe, and not for a given geometry only but as a subroutine in a code optimising the shape of the aircraft, and so on. Because of this, RANS etc. will always be there as the means of saving computing time. Except, of course, someone will give an ultimate solution to the problem, thus replacing the methods available now .

Well, a morning essay is what I produced. Hope, no harm done.

Sergei