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

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

Hi Outi,

check how we compute the derivatives in wgradm1().
In general strong 2nd derivates d/di [d/dj u] can be computed by a sequence of wgradm1() and dssum().

Example: d/dx[ d/dy u ], d/dy [ d/dy u], d/dz [ d/dy u]

call wgradm1(uddx,uddy,uddz,u,nelt)
call vec_dssum(uddx,uddy,uddz,nx1,ny1,nz1)
call wgradm1(ud2dx,ud2dy,ud2dz,uddy,nelt)
all vec_dssum(ud2dx,ud2dy,ud2dz,nx1,ny1,nz1)

You're right the derivatives are in general not in H1 because there are not in C0. That's why you need to call dssum() to make the derivative field continuous across elemental boundaries.


Stefan

On May 25, 2010, at 11:30 AM, 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
> 
> 
> 
> 
> 
> 
> 
> _______________________________________________
> Nek5000-users mailing list
> Nek5000-users at lists.mcs.anl.gov
> https://lists.mcs.anl.gov/mailman/listinfo/nek5000-users