in which years did LES and DNS come into being? Shuo

Around the begining of the 1900 years, for the concept of Direct Numerical Simulation. But I'm not be very sure. If you considere the work of Fourrier and Taylor, we can considere that numerical simulation is very old...

But if you considere the first simulation on computer maybe around 1950 for DNS. And if you considere the question of the first LES model (Smagorinsky) it's around 1965. If you want a very good review about turbulence i invite you to read the excellent book of Marcel Lesieur.

regards,

DNS calculations in 1950? Considering the "computers" that were available at this time, this seems strange. Even 1965 for LES is astonishingly early. On what kind of system was the first LES done then?

For the first LES is very simple : Smagorinsky model. The concept of eddy diffusivity is very old and since 1963 J. Smagorinsky propose a relation for estimate is value. (J. Smagorinsky General circulation experiments with the primitive equations, Mon. Weather Rev, 91). But the concept of 'eddy diffusivity' is more old. My talk is only about the first 'beta' simulation. And since 1970, Deardorff obtained some good result for the turbulent channel flow.

For the first DNS, i'm understand what you mean. Maybe the it's wrong. I don't try something very clear around this point. The first simultion on computer was in the end of 50's. But what can you simultion ... i don't know.

Sorry, (i don't read me before i post :x)

For the first DNS, i'm understand you. Maybe the it's wrong. I don't try something very clear around this point. The first simulation on computer was in the end of 50's. But what sort of simulation ... i don't know. Flow simulation, and something around Navier Stokes resolution, but maybe with lot of approximation

Smagorinsky's model is just a modified version of that of Neumann (also Prandtl) and was introduced to stabilize the numerical finite difference problem - current interest in MILES highlights this. I'm not too sure when the concept of LES was formulated but there was a paper in JFM (1969) which explicitly discusses LES by name - this work probably originated some time after Lilly's paper which followed from that of Smagorinsky (around 1966/7).

As for DNS (this is just a renaming of unsteady laminar flow solvers) and so you could say the first real work on this was Richardson in the 1920's. First significant/practical application using a computer was probably

Charney, J. G., R. Fjörtoft and John von Neumann. 1950. "Numerical Integration of the Barotropic Vorticity Equation", Tellus, Vol. 2, pp. 237-254.

That is really interesting that John von Neumann himself did these calculations on then ENIAC. Just look at the picture of this system. Thank you Tom, looking for the reference your mentioned i found this interesting link:

http://www.aip.org/history/sloan/gcm/prehistory.html "The Meteorology Project ran its first computerized weather forecast on the ENIAC in 1950. The group's model, like Richardson's, divided the atmosphere into a set of grid cells and employed finite difference methods to solve differential equations numerically. The 1950 forecasts, covering North America, used a two-dimensional grid with 270 points about 700 km apart. The time step was three hours."

thank you very much Tom you are very clear (not like me)

Just for history, I know that Smagorinsky work for a 2D turbulence atmospheric problem. Like you know, this model doesn't match for this kind of turbulence and he was unhappy but fiew years later ...

For LES ..the concept of 'numerical viscosity ' is very old. But the filtering operation is around 70's.

Yes the definition of the filter was, I think, in the 70's - although you could argue that it's nothing more than glorified Reynolds averaging in space. Basically the definition of the filter was an attempt to rationalize what people (mainly Meteorologists at that time) were doing in simulations of the atmospheric boundary-layer. Since then a lot of research (e.g. dynamic models, stochastic backscatter,...) has been about undoing the excessive dissipation of the Smagorinsky model.

The actual form of, what is now called the Smagorinsky model, can actually be deduced from the Reiner-Rivlin model for a non-Newtonian fluid (they worked out the general formula for the stress tensor).

The break through with DNS came with the work of Orszag in the early 1970 I think, look for his papers in J. Fluid Mech. and Phys. Fluids. He developed the pseudospectral methods.

Sorry, I couldn't resist.