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Hi Arnold,
<div><br>
</div>
<div>The velocity is only in C^0, which means it is continuous. The first derivative</div>
<div>is defined everywhere, but is discontinuous, meaning that the vorticity is</div>
<div>discontinuous.</div>
<div><br>
</div>
<div>The derivative of the vorticity involves the second derivative of velocity, and this</div>
<div>is not defined.</div>
<div><br>
</div>
<div>All that being said, the vorticity will converge to a continuous function exponentially</div>
<div>fast with increasing polynomial order. So if you want to differentiate the vorticity</div>
<div>you have the option of increasing the polynomial order. </div>
<div><br>
</div>
<div>Alternatively, you can try to regularize the vorticity prior to differentiating it.</div>
<div>A common strategy is to call dsavg( . ) for each component of vorticity -- which</div>
<div>makes it continuous, but this wouldn't necessarily make the derivatives better.</div>
<div>Other alternatives would be to use a combination of dsavg() and some type of</div>
<div>low-pass filtering, e.g., by solving a Helmholtz problem of the form (I-L^2 \nabla^2) vbar = v,</div>
<div>where L is the filter length. Another option is to look at the context in which</div>
<div>you want to use your differentiated vorticity. Perhaps this can be recast in a weak</div>
<div>form, in which one of the derivatives is moved onto the (continuous and differentiable)</div>
<div>test functions, etc.</div>
<div><br>
</div>
<div>hth,</div>
<div><br>
</div>
<div>Paul</div>
<div><br>
<div style="font-family: Times New Roman; color: #000000; font-size: 16px">
<hr tabindex="-1">
<div id="divRpF849118" style="direction: ltr;"><font face="Tahoma" size="2" color="#000000"><b>From:</b> nek5000-users-bounces@lists.mcs.anl.gov [nek5000-users-bounces@lists.mcs.anl.gov] on behalf of nek5000-users@lists.mcs.anl.gov [nek5000-users@lists.mcs.anl.gov]<br>
<b>Sent:</b> Friday, March 03, 2017 6:02 AM<br>
<b>To:</b> nek5000-users@lists.mcs.anl.gov<br>
<b>Subject:</b> [Nek5000-users] Problem with Spatial Derivatives of field<br>
</font><br>
</div>
<div></div>
<div>
<p>Hi Neks,</p>
<p>I'm having some problems with computing the gradients of vorticity. <br>
</p>
<p>So what I do in the usercheck is something like : <br>
</p>
<p><br>
</p>
<p><br>
</p>
<p>call call comp_vort3(vort,work1,work2,vxp,vyp,vzp) ! Computing vorticity of perturbations
<br>
</p>
<p>call gradm1(derivvortx,derivvorty,derivvortz,vort(1,1)) <br>
</p>
<p><br>
</p>
<p><br>
</p>
<p>However, by doing this I do observe some abnormal results when I plot the fields : derivvortx, derivvorty, derivvortz.</p>
<p>Attached you will find a snapshot of the magnitude of derivvortx and derivvorty (obtained using paraview)</p>
<p>I am wondering why I am having extremely high values a the boudary of the elements. Has anyone noticed or faced such a problem?
<br>
</p>
<p><br>
</p>
<p>Even when I increase lx1, reduce dt and reduce the mesh size, the problem remains..</p>
<p><br>
</p>
<p>Thank you for your time,</p>
<p>Best wishes,</p>
<p><br>
</p>
<p>Arnold<br>
</p>
<p><br>
</p>
<p><br>
</p>
<p><br>
</p>
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