[Nek5000-users] Contents of Nek5000-users digest, Vol 99, Issue 14 Message 1

[nek5000-users at lists.mcs.anl.gov]

Hi Daniel,

Technically, you need 1.5x in each direction.  This generally proves to be overly conservative,
however.

Yes - if you set param 103 in the .rea file to be 0.1, it will remove 10% of the energy
in the Nth mode at every time step, which gives a reasonably effective grid-scale filter
that is also relatively benign when you are well resolved.

If your N is large ( > 8, say) then I would set param 101 = lx1/5 or lx1/6.    p101 controls
the number of modes, in addition to the Nth one, that are touched by the filter.  The filter
is applied with a parabolic round-off of the form:

sigma =  1 - p103 * [  (k-k_cut) / (lx1-k_cut) ]^2   for k > k_cut,   sigma = 1, otherwise,

where k_cut = p101+1.

So, when k=lx1, you have sigma = 1-p103  (=0.9 if p103=0.1)

when k = k_cut,  sigma = 1.

The significance of sigma is that it is the multiplier in the modal filter basis, given by:

phi_k(x) = L_k(x) - L_{k-1}(x), for k=2,...,lx1,

So, expanding 

   u(x) = \sum_k u^k phi_k

we construct the filtered solution as

   ubar(x) = sum_k  sigma_k  u^k  phi_k(x)

Obviously, if all the sigmas = 1, then ubar == u.

Common values are to run with p103=.05, p101=0, depending on resolution.


Paul

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From: nek5000-users-bounces at lists.mcs.anl.gov [nek5000-users-bounces at lists.mcs.anl.gov] on behalf of nek5000-users at lists.mcs.anl.gov [nek5000-users at lists.mcs.anl.gov]
Sent: Monday, May 22, 2017 8:01 AM
To: nek5000-users at lists.mcs.anl.gov
Subject: Re: [Nek5000-users] Contents of Nek5000-users digest, Vol 99,  Issue 14 Message 1

Hi Paul,

thank you very much for your quick and detailed answer.
I have might ask you two follow up questions.

1) Is the following statement correct?
In order to compare my energy spectrum with literature values, I therefore
have to use pi/2 times more points to have an identical kmax.

2) Not really in the same context, but why is the energy spectrum of
"coarse DNS" almost identical to a fully resolved DNS? Are Pope's
resolution recommendations too conservative for NEK, so that the
Kolmogorov scales can be captured with significant less points or are
there some routines in the background that prevent a growing instability
in the high modes, if the dissipation regime is under resolved?

Thanks,

Daniel
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