Dear all,

RE: Can I use the unsteady RANS result as an initial solution for LES?

I am trying to do LES with a SIMPLE based method code. For RANS calculation, I usually use the fully implicit scheme in time and the hybrid scheme in space, hence I could use very large time step and get the results quickly. However, for LES simulation, I was told that I will have to use the Crank-Nicolson scheme in time and the central difference scheme in space. I find that I can only use very small time step. My question is: can I use the unsteady RANS solution as an initial input for my LES simulation ? By doing this, can I get a LES solution much quicker ?

Thank you very much for your reply in advance.

Li

Hi,

Yes you can. To improve things you can also try to randomly add small velocity fluctuations to the flow field (based upon turbulence intesity). An alternative would be to run LES with a large time step & hybrid scheme for a few sweeps then change to central. Actually, if and your time step duration is small enough to keep the CFL number below 1, the hybrid scheme will revert to central.

Tim

Dear Tim,

Your reply is really helpful. Thank you very much indeed.

Could you please specify the method more in detail about how large the the small random velocity fluctuations should be or direct me to any references ? Could you also please tell me why I cannot use fully implicit scheme in time for LES ?

Thank you again.

Li

Quite simple. If you take the fluctuations too large your computation will crash. If you take the fluctuations too small the flow will become laminar after some time. Say the fluctuations are about 10% of the mean velocity, that's probably OK. Anyway, you have to run your computations for quite a long time because the flow has to become independent of the initial field. The initial field is never real turbulence.

You have to resolve the turbulent motions also in time and therefore there are limitations for the time step. Most of the people use explicit schemes for the nonlinear part because the time step is limited anyway because of physical reasons and a explicit scheme is computationally much cheaper.

Tom

Could you please specify the method more in detail about how large the the small random velocity fluctuations should be or direct me to any references ?

Technically you should try to represent the spectrum of fluctuations at the inlet and let them propogate through the domain. However this takes a long time. Adding velocity fluctuations to the entire domain is an approximation - I just use random number x turbulence intensity x flow velocity. This is easy but not entirely correct because you do not match the fluctuation spectrum correctly (my view is that the simulation will sort this out fairly rapidly). I think you can use a fairly wide range of values - too big & you have stability problems but these tend to dissipate out too small and you have to wait for them to build up in the solution. However I think using even a really small intensity value is better than nothing.... I cant find the appropriate reference at the mo.

Could you also please tell me why I cannot use fully implicit scheme in time for LES ? - You can use fully implicit - I do so I hope you can!!! you just have to be aware that two stability limits apply to large-eddy simulations.

The ï¬�rst is the viscous condition, that requires that time-step ∆t be less than ∆t = ¥ò∆y2/¥í (where ¥ò depends on the time advancement chosen).

The CFL condition requires that ∆t be less than ∆t = CFL∆x/u, where the maximum allowable Courant number CFL also depends on the numerical scheme used (I use approx 0.25 ).

Finally, the physical constraint requires ∆t to be less than the time scale of the smallest resolved scale of motion, ¥ó ¡* ∆x/Uc (where Uc is a convective velocity of the same order as the outer velocity). In many cases (especially in wall-bounded flows, and at low Reynolds numbers)

The viscous condition demands a much smaller time-step than the other two; for this reason, the diffusive terms of the governing equations are often advanced using implicit schemes (typically, the second-order Crank-Nicolson.

hope this is of some help to you

Tim.