FLUENT控制步长时间courant数的有效的经验

" What is the difference between the time accurate solution of Navier-Stokes equations and the DNS solution? "

I'm not sure I understand this question correctly, but as far as I am aware DNS (Direct Numerical Simulation) is defined as a time accurate solution of the Navier-Stokes equations.

Perhaps you mean "What is the difference between laminar & turbulent DNS?" ? Believing this to be so from reading the rest of your message I wrote the following:

When the DNS is of turbulence rather than a laminar flow the turbulence requires initialization in some way. The same is true of LES (LES is always turbulent, because laminar LES = DNS by definition). I have found little reported work on the proceedures used to accomplish this turbulence initialization.

I can only speak for the LES code I use (and the generations of code that preceded it). The turbulence is initialized by setting an initial flow field that has a random fluctation velocity component added to the inital mean velocity.

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For example:

U_initial_cell =

U_initial_mean + (Random_number * U_initial_mean * 0.20)

( Random_number has a value in the range -1 to +1 )

This function sets the initial cell velocity to that of the initial_mean with a tolerance of 20% (i.e. + or - 20%). So if the U_initial_mean was 1.0 then the initial velocity of the cell could be anywhere between 0.8 and 1.2 depending on the Random_number (an intrinsic computer function).

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The value for initial fluctuation (20% etc) is a fairly arbitrary value just required to `kick-start' the turbulence. Once the simulation has been kick-started and run sufficiently long enough for the correct energy cascade to be observed (by monitoring k.e. of the flow) the statistics data from that point onward is o.k to be used for results. This accumulation of statistical data is one of the reasons why LES/DNS turbulent simulations require so much more time to run.

Providing the same random_number is used on the same cells during initialization the computations of two DNS cases will be exactly* the same when all other conditions (boundary, geometry, etc) are equivalent.

*exactly is defined as Phi(x,t)_simulation_A = Phi(x,t)_simulation_B

If different random_numbers are used then the flow solution would be expected to be slightly numerically different from a previous run, but statistically the same. This would be similar to the case where two experimental turbulent simulations in a wind tunnel do not have exactly* the same flow field, but are expected to be statistically the same and have the same coherent structures in the flow.

LES, or turbulent DNS is like journeying along a road. The intial fluctations imposed pre-determine which exact roads you will travel on, and the other boundary conditions determine the general direction in which you will be heading. In industrial problems the concern is with the direction you are heading,

N,E,S, or West, and not so much if you are on a particular road at a particular time, e.g. walking by 43 Accacia Road at 5pm.

This idea may be seen in the definition of turblence by Hinze (1959) "...so that statistically distinct average values can be discerned." For if Taylor & Von Karman's 1937 definition was taken literally CFD shouldn't exist!

The grid size of LES should be small enough. But it is not easy to get the exact size of the smallest cells. Some people use y+, other people use Kolmogorov scales,etc. As you know, the basic assumption is that the flow with SGS is isotropic in the case of using Smagorinsky model.

Based on my experience, not only the size of smallest grids but also there are many other facts to be considered in LES. Computational domain size, cell cluster, boundary conditions, wall treatment, etc.

So if you want to do LES, some compromise would be necessary. At first, please use reasonable size of computational domain, number of cells and run the problem in your computer. If the result is not accurate enough, then increase the resolution. But even though the resolution is not enough (in the LES viewpoint), you may get satisfactory results.

Good luck