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

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

I am afraid that's not correct. This way you compute the weak laplacian and you're missing the boundary term.  

Stefan


On May 25, 2010, at 12:00 PM, nek5000-users at lists.mcs.anl.gov wrote:

> Hi Outi,
> 
> You can use
> 
> call sethlm(h1,h2,intype)  ! intype = 0 gives laplacian
> 
> call axhelm(vx2,vx,h1,h2,1,1)   ! d^2(u)dx^2 + d^2(u)dy^2 + d^2(u)dz^2
> 
> 
> Johan
> 
> 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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> 
> 
> -- 
> Johan Ohlsson
> Department of Mechanics, KTH
> SE-100 44, Stockholm, Sweden
> Phone: +46 8 7906876
> E-mail: johan at mech.kth.se
> 
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