[Nek5000-users] Problem with Spatial Derivatives of field

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

Hi Arnold,

The velocity is only in C^0, which means it is continuous.  The first derivative
is defined everywhere, but is discontinuous, meaning that the vorticity is
discontinuous.

The derivative of the vorticity involves the second derivative of velocity, and this
is not defined.

All that being said, the vorticity will converge to a continuous function exponentially
fast with increasing polynomial order.   So if you want to differentiate the vorticity
you have the option of increasing the polynomial order.

Alternatively, you can try to regularize the vorticity prior to differentiating it.
A common strategy is to call dsavg( . ) for each component of vorticity -- which
makes it continuous, but this wouldn't necessarily make the derivatives better.
Other alternatives would be to use a combination of dsavg() and some type of
low-pass filtering, e.g., by solving a Helmholtz problem of the form  (I-L^2 \nabla^2) vbar = v,
where L is the filter length.   Another option is to look at the context in which
you want to use your differentiated vorticity.   Perhaps this can be recast in a weak
form, in which one of the derivatives is moved onto the (continuous and differentiable)
test functions, etc.

hth,

Paul

________________________________
From: nek5000-users-bounces at lists.mcs.anl.gov [nek5000-users-bounces at lists.mcs.anl.gov] on behalf of nek5000-users at lists.mcs.anl.gov [nek5000-users at lists.mcs.anl.gov]
Sent: Friday, March 03, 2017 6:02 AM
To: nek5000-users at lists.mcs.anl.gov
Subject: [Nek5000-users] Problem with Spatial Derivatives of field


Hi Neks,

I'm having some problems with computing the gradients of vorticity.

So what I do in the usercheck is something like :



call call comp_vort3(vort,work1,work2,vxp,vyp,vzp)   ! Computing vorticity of perturbations

call gradm1(derivvortx,derivvorty,derivvortz,vort(1,1))



However, by doing this I do observe some abnormal results when I plot the fields : derivvortx, derivvorty, derivvortz.

Attached you will find a snapshot of the magnitude of derivvortx and derivvorty (obtained using paraview)

I am wondering why I am having extremely high values a the boudary of the elements. Has anyone noticed or faced such a problem?


Even when I increase lx1, reduce dt and reduce the mesh size, the problem remains..


Thank you for your time,

Best wishes,


Arnold




--

[cid:part1.AAFA1EB3.C1F7AC72 at onera.fr]Arnold Wakim
Doctorant,
Département d´Aérodynamique Fondamentale et Expérimentale
Tél: +33 1 46 23 51 83

ONERA - The French Aerospace Lab -Centre de Meudon
8, rue des Vertugadins - 92190 MEUDON

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