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Dear Johan,
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<div>Actually - I was mistaken.</div>
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<div>What we use is:</div>
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<div> d/dn (u_i) = 0 </div>
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<div>for i=1,...,3</div>
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<div>We could however (and sometimes do) require Neumann only on the normal velocity component --</div>
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<div>grad (phi) . nhat = 0</div>
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<div>where phi = U . nhat</div>
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<div>The tangential components can be prescribed. That is the capability provided by the "on "</div>
<div>BC.</div>
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<div>Paul</div>
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<div id="divRpF730965" 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> Thursday, October 06, 2016 6:58 AM<br>
<b>To:</b> nek5000-users@lists.mcs.anl.gov<br>
<b>Subject:</b> Re: [Nek5000-users] Open Boundary condition in NEK user Documentation<br>
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<p>Thank you for a good answer!</p>
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<p>Just to clarify, is it in LaTeX written as this:</p>
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<p>(\hat{n} \cdot \nabla)(u \cdot \hat{n}) = 0 ?</p>
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<p>If the wall normal is in the z-direction, then the open boundary condition for the velocity is:<br>
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<p>d/dz u_z = 0?</p>
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<p>Best regards,</p>
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<p>Johan<br>
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<div id="divRplyFwdMsg" dir="ltr"><font color="#000000" face="Calibri, sans-serif" style="font-size:11pt"><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> Thursday, October 6, 2016 12:40 PM<br>
<b>To:</b> nek5000-users@lists.mcs.anl.gov<br>
<b>Subject:</b> Re: [Nek5000-users] Open Boundary condition in NEK user Documentation</font>
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Dear Johan,
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<div>The outflow boundary condition, 'O ', is indeed the same as 'I ' for the thermal problem</div>
<div>since they both enforce grad T . nhat = 0.</div>
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<div>However, both also admit thermal flux by advection for cases where U . nhat is > 0, and that is</div>
<div>the intent of outflow --- to allow thermal flux to be carried out.</div>
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<div>For velocity, the situation is a bit more delicate. To leading order, however, 'O ' imposes</div>
<div>d/dn (U.nhat) = 0 and p=0. That is, Neumann conditions for the viscous fluxes and Dirichlet</div>
<div>for pressure.</div>
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<div>hth,</div>
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<div>Paul</div>
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<div id="divRpF973935" style="direction:ltr"><font size="2" color="#000000" face="Tahoma"><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> Thursday, October 06, 2016 4:59 AM<br>
<b>To:</b> nek5000-users@lists.mcs.anl.gov<br>
<b>Subject:</b> [Nek5000-users] Open Boundary condition in NEK user Documentation<br>
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<p>Dear Neks,</p>
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<p>I am trying to understand what is actually meant by an "open boundary" in Nek.</p>
<p>Un the user documentation, eqn (4.5) sais that, for the temperature, it is</p>
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<p>grad(T) dot n = 0, where n is the normal to the boundary.</p>
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<p>Since the heat flux is q = - grad(T), I would rather interpret this as a zero flux boundary condition.</p>
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<p>And indeed, the insulated boundary described by equation (4.6) is identical to the open boundary condition.</p>
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<p>Is equation (4.5) a type-O or is the open boundary for the temperature actually the same as an insulated boundary?</p>
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<p>Also: Should not the open boundary condition for the "no-stress forumlation" also be given by the same expression as for the "stress-formulation" eqn (4.2)?<br>
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<p>Best Regards,</p>
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<p>Johan<br>
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