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

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

Thanks to everybody for answers. I will proceed tomorrow and see which  
one I should implement (I am going away for a conference trip, and  
will return with possible follow-up questions in June).

Just a quick comment to the suggestion below, on solving the linear  
stability problem also in Nek5000:
I would be interested to do that, and I have heard there exists a  
linear version of Nek5000 which could be used. However, then the ALE- 
formulation would also need to be linearised around the steady  
position of the interface. Is that done already, or could that be done?

Also very interesting would be to calculate the steady state with  
surface tension in Nek5000. I have two media (say, water and air), the  
stresses of which need to be coupled on an interface involving surface  
tension, which I assume is possible in the stress formulation. The  
boundary conditions that I use would then not stabilise the time- 
dependent flow field anymore, but I assume one could use some sort of  
filtering, or an iterative procedure instead of ALE formulation.

Regards,
Outi

25 maj 2010 kl. 13.39 skrev 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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