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

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

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