Hi all!

My questions are about the DNS world. First of all, it is always said that the grid made for a DNS simulation must be suitable to cover all lenght and time scales.

The question is: imagin that I have in my home a computer that has 1000Terabytes of RAM and a similar HDD with a n-th processors. Then I want to make a DNS simulation of a flow past a car, with V=30m/s and reference lenght of L=4.1. The smallest length scale would be the kolmogorov one, and it is calculated by: l=(v^3/epsilon)^(1/4), being epsilon the dissipation scale, (which is proportional to U^3/L, U=mean flow velocity and L=length scale) and v the kinematic viscosity (for the air,v=1.5e-5)

With these parameters is it correct to say that my smallest length scale will be l=[(1.5e-5)^3/(30^3/4.1)]=0.0268mm? If so, it means that the smallest length of my grid must be <0.0268mm??

And the last question: what happens if in a DNS we don't discretize the flow domain with elements with a suitable length?I mean, what happens if the elements size is too coarse that the grid does not cover the smallest scales? Does the solution diverge? Or does it only give a solution that is not as good as it would be with a finer grid?

Thanks a lot to all!

Regards, Freeman

If your calculations are right you need 15293 points in 1 dimension so you need 3576663358757 grid-point!!! Regarding the second question If the grid is coarse you aren't performing a DNS but a LES no-model (that means a bad DNS)!

Hi Mar,

Well, I guess with your reply that the calculation of the minimum lenght of the grid is well done, isn't it?

By the way it eould be necessary to build a grid with uniform-spaced points, so the number of grid points may be less.

Thanks for your participation.

Hi,

You use the relation U^3/L (Taylor's assumption) to calculate the Kolmogorov length scale, but in this relation you have to use turbulence quantities (U: turbulent vel. fluctuations and L: integral length scale), not the mean flow characteristics. In the DNS, the grid spacing should indeed scale with the Kolmogorov length scale. In a well resolved DNS the grid spacing is about 3 times the Kolmogorov length scale.

About the physics: in a turbulent boundary layer, the production of turbulence due to the mean shear is approx. balanced by dissipation. If the small (dissipation) scales are not resolved (and the cascade is interrupted), the produced energy cannot be dissipated and turbulent energy will accumulate: the computation will crash. The remedy is to introduce then to introduce numerical diffusion, a subgrid scale model, filter etc.

Wow Tom, I liked a lot your explanation about the physics: really clear! Thanks a lot!

You say that in the Taylor's assumption, U is the magnitude of the velocity fluctuation, but if I ever wanted to make a DNS in a fully turbulent flow case (like a flow past a bluff body or similar), how would I know the grid spacing with anticipation if I don't know these velocity fluctuations before making the simulation? I mean, how can I make a realistic calculation on how fine must be my grid in a DNS.

Thank you for your help.

Regards, Freeman

Hi,

Usuall, U scales with the mean flow (for example in pipe and boundary layer flow, about 0.1 times the mean flow) and this scaling is Re independent approx. To estimate U, results from experiments or previous simulations can thus be used.

By the way, it is not uncommon in DNS that the resolution is checked after the simulaties has been carried out. It is not always possible to estimate the dissipation accurately.

Thanks Tom, your replies are really appreciated. You say that it is uncommon in DNS that the resolution is checked after simulations, but i've heard that grid points are related to the Re number with a relation Re^(9/4) if my memory serves me well: how it can be demonstrated in few lines this order of magnitude of the grid.

And another thing: if the shortest length scale cannot be calculated by anticipation in order to know the shortest length in the grid, a DNS meshing is a try-and-error activiity? Because you said that if the shortest length scales are not well resolved in the mesh (by having a coarse mesh) DNS will crash ("diverge"), won't it?

Thanks a lot for your input!