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<p>Hi Paul, <br>
</p>
<p><br>
thank you very much for the detailed problem description and the
laminar test case. <br>
<br>
<br>
Best Regards,<br>
Steffen<br>
</p>
<br>
<blockquote type="cite"
cite="mid:mailman.643.1501193704.6680.nek5000-users@lists.mcs.anl.gov">
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<div class="headerdisplayname" style="display:inline;">Subject:
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Re: [Nek5000-users] Only neumann and periodic boundary
conditions for energy equation</td>
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<div class="headerdisplayname" style="display:inline;">From:
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<a class="moz-txt-link-rfc2396E" href="mailto:nek5000-users@lists.mcs.anl.gov"><nek5000-users@lists.mcs.anl.gov></a></td>
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<div class="headerdisplayname" style="display:inline;">Date:
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07/27/2017 10:22 PM</td>
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<div class="headerdisplayname" style="display:inline;">To:
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<a class="moz-txt-link-rfc2396E" href="mailto:nek5000-users@lists.mcs.anl.gov">"nek5000-users@lists.mcs.anl.gov"</a>
<a class="moz-txt-link-rfc2396E" href="mailto:nek5000-users@lists.mcs.anl.gov"><nek5000-users@lists.mcs.anl.gov></a></td>
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<p>Hi Steffen,</p>
<p><br>
</p>
<p>The attached file shows how to deal with the case</p>
<p>you're interested in. </p>
<p><br>
</p>
<p>Please see the README, the .pdf, and the .usr files.</p>
<p><br>
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<p>hth,</p>
<p><br>
</p>
<p>Paul</p>
<br>
<br>
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style="font-size:11pt" color="#000000" face="Calibri,
sans-serif"><b>From:</b> Nek5000-users
<a class="moz-txt-link-rfc2396E" href="mailto:nek5000-users-bounces@lists.mcs.anl.gov"><nek5000-users-bounces@lists.mcs.anl.gov></a> on
behalf of <a class="moz-txt-link-abbreviated" href="mailto:nek5000-users@lists.mcs.anl.gov">nek5000-users@lists.mcs.anl.gov</a>
<a class="moz-txt-link-rfc2396E" href="mailto:nek5000-users@lists.mcs.anl.gov"><nek5000-users@lists.mcs.anl.gov></a><br>
<b>Sent:</b> Thursday, July 27, 2017 2:11 AM<br>
<b>To:</b> <a class="moz-txt-link-abbreviated" href="mailto:nek5000-users@lists.mcs.anl.gov">nek5000-users@lists.mcs.anl.gov</a><br>
<b>Subject:</b> [Nek5000-users] Only neumann and
periodic boundary conditions for energy equation</font>
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<font size="2"><span style="font-size:10pt;">
<div class="PlainText">Hi Neks,<br>
<br>
I want to simulate "ideal" isoflux boundary conditions
in a pipe.<br>
As the temperature (T) increases in streamwise
direction (in my case <br>
z-direction), I define<br>
theta(r,phi,z,t) = (<T_w>(z) - T(r,phi,z,t))/T_r<br>
with T_r = q_w/(rho c_p U_b) and <T_w>(z)
denoting the time average of <br>
the wall temperature T_w.<br>
<br>
With that I can recast my energy equation to solve for
the temperature <br>
difference theta instead of the temperature T which
allows for periodic <br>
boundary conditions as theta does not change in
streamwise direction. <br>
This introduces an additional source term 4 u_z.<br>
<br>
I would like to set a constant heat flux boundary
condition at the wall <br>
(see e.g. Piller: Direct numerical simulation of
turbulent forced <br>
convection in a pipe. 2005), i.e. a Neumann boundary
condition (ideal <br>
isoflux), and compare the results to those obtained
with the same PDE <br>
but a Dirichlet boundary condition theta_w=0
(mixed-type). This setup of <br>
applying only Neumann boundary conditions is
"ill-posed". I believe <br>
because there is no unique solution to this setup,
right?<br>
As Piller points out, one can introduce an additional
constraint and <br>
enforce the volume averaged temperature to be constant
to overcome this <br>
issue. Piller did not face this problem as he was
using a finite volume <br>
method.<br>
<br>
I can calculate the volume integral over temperature
like this, correct?<br>
nt = nx1*ny1*nz1*nelt<br>
t_vol = glsc2(t, bm1, nt)<br>
<br>
And then I would adjust my source term in each step to
keep t_vol=constant.<br>
However, I do not know this constant in advance. If I
set it to an <br>
arbitrary value, e.g. zero, this leads to negative
theta at the wall, <br>
which contradicts my definition of theta.<br>
<br>
<br>
I know this is not a specific Nek5000 Problem but
maybe someone has <br>
experienced similar issues and found a solution that
works in Nek5000?<br>
<br>
Best Regards,<br>
Steffen Straub<br>
<br>
-- <br>
Karlsruhe Institute of Technology (KIT)<br>
Institute of Fluid Mechanics<br>
<br>
M.Sc. Steffen Straub<br>
Doctoral Researcher<br>
<br>
Kaiserstraße 10<br>
Building 10.23<br>
76131 Karlsruhe, Germany<br>
<br>
Phone: +49 721 608-43027<br>
E-mail: <a class="moz-txt-link-abbreviated" href="mailto:steffen.straub@kit.edu">steffen.straub@kit.edu</a><br>
Web: <a href="http://www.istm.kit.edu"
id="LPlnk80880" previewremoved="true"
moz-do-not-send="true">http://www.istm.kit.edu</a><br>
<br>
KIT – The Research University in the Helmholtz
Association<br>
<br>
Since 2010, the KIT has been certified as a
family-friendly university.<br>
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