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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>
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<p>hth,</p>
<p><br>
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<p>Paul</p>
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<div id="x_divRplyFwdMsg" dir="ltr"><font face="Calibri, sans-serif" color="#000000" style="font-size:11pt"><b>From:</b> Nek5000-users <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> Thursday, July 27, 2017 2:11 AM<br>
<b>To:</b> nek5000-users@lists.mcs.anl.gov<br>
<b>Subject:</b> [Nek5000-users] Only neumann and periodic boundary conditions for energy equation</font>
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<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: steffen.straub@kit.edu<br>
Web: <a href="http://www.istm.kit.edu" id="LPlnk80880" previewremoved="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>
<br>
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