[Nek5000-users] Time step independence

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

Good morning all,

I'm relatively inexperienced with DNS simulations, so I'd appreciate your
help with the following:

Are there any tests specific to Nek that can be run to determine whether
the solution is independent of the time step length? I've attempted a
couple of approaches, including:

i.) Running for extended periods of time with different fixed time step
lengths before using avg_all to calculate velocities and other statistical
parameters and then comparing for the different time step lengths.
ii.) Calculate the spectra from the velocity magnitude and check whether it
is resolving past the -5/3 inertial range. This seems to be the case, as
beyond a certain frequency the slope becomes more negative as is the
general expectation in the dissipation scale range.
iii.) I'm using a subroutine I wrote to calculate the minimum Kolmogorov
time and length scales in the domain and comparing those values with my
time step length and maximum grid spacing, so as to ensure that those
parameter maxima are still smaller than the minimum Kolmogorov scales.

Would any of these approaches suffice when making an explicit statement of
time step independence? I am at the beginnings a draft manuscript for a
publication relating to the work, and I understand that to claim DNS we
have to be rigorous in terms of conforming to all the requirements, so I
want to get it right from the start.

Thanks in advance for your help!

Lambert
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