[Nek5000-users] A good way to approximate second derivatives?

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

Hi Outi,

Nek5000 supports free-surface motion and does not require
2nd derivatives, using the same approach that is used for
the 2nd-order Laplace operator, namely, by transfering one
of the derivatives to the test functions.

The description of the implementation can be found in Lee W. Ho's
MIT thesis

http://dspace.mit.edu/handle/1721.1/14293

Note that one of our example problems, fs_hydro, implements
a linear stability test with results described in

  www.mcs.anl.gov/~fischer/users.pdf

I'm not certain if this is what you're needing?

Paul



On Tue, 25 May 2010, nek5000-users at lists.mcs.anl.gov wrote:

> Hello!
>
> This is the first time I write to this list.
> I am a PhD student at KTH Mechanics, and use Nek5000 mostly to get steady 
> solutions for my linear stability calculations (where the steadiness is 
> imposed geometrically, by boundary conditions) on 2D wakes and jets. The 
> stability calculation is performed on a different grid, in another code.
>
> I wrote a script where I interpolate the solution form Nek5000 exactly to my 
> stability grid using the Legendre basis functions, and for the flow variables 
> (U,V,P) and their first derivatives this works fine. However, now I am using 
> the same steady solution to calculate stability with surface tension (since 
> for slowly developing flows the steady state without surface tension can 
> still be used). In this new setting, the second derivatives (Uxx,Uyy,Vxx,Vyy) 
> are also needed.
>
> Therefore I wonder if there is any standard way to approximate the second 
> derivatives of the flow variables in Nek5000?
> The basis functions are only C1-continuous across the element boundaries, and 
> even if they would have been continuous, the second derivatives are always 
> noisy, e.g. if taken from experimental data.
> Currently I use finite differences combined with a smooth function in Matlab 
> with a 5-point moving average.
>
> Thank you for input or better ideas,
>
> Outi Tammisola
>
>
>
>
>
>
>
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