<html>
<head>
<meta http-equiv="Content-Type" content="text/html; charset=iso-8859-1">
<style type="text/css" style="display:none;"><!-- P {margin-top:0;margin-bottom:0;} --></style>
</head>
<body dir="ltr">
<div id="divtagdefaultwrapper" style="font-size:12pt;color:#000000;background-color:#FFFFFF;font-family:Calibri,Arial,Helvetica,sans-serif;">
<p>Thank you,</p>
<p><br>
</p>
<p>this makes sense to me.</p>
<p><br>
</p>
<p>/Johan<br>
</p>
<br>
<br>
<div style="color: rgb(0, 0, 0);">
<hr tabindex="-1" style="display:inline-block; width:98%">
<div id="divRplyFwdMsg" dir="ltr"><font style="font-size:11pt" color="#000000" face="Calibri, sans-serif"><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 2:22 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>
<div> </div>
</div>
<div>
<div style="direction:ltr; font-family:Tahoma; color:#000000; font-size:10pt">
<div><br>
</div>
Dear Johan,
<div><br>
</div>
<div>Actually - I was mistaken.</div>
<div><br>
</div>
<div>What we use is:</div>
<div><br>
</div>
<div> d/dn (u_i) = 0 </div>
<div><br>
</div>
<div>for i=1,...,3</div>
<div><br>
</div>
<div>We could however (and sometimes do) require Neumann only on the normal velocity component --</div>
<div><br>
</div>
<div>grad (phi) . nhat = 0</div>
<div><br>
</div>
<div>where phi = U . nhat</div>
<div><br>
</div>
<div>The tangential components can be prescribed. That is the capability provided by the "on "</div>
<div>BC.</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="divRpF730965" 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 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>
</font><br>
</div>
<div></div>
<div>
<div id="divtagdefaultwrapper" style="font-size:12pt; color:#000000; background-color:#FFFFFF; font-family:Calibri,Arial,Helvetica,sans-serif">
<p>Thank you for a good answer!</p>
<p><br>
</p>
<p>Just to clarify, is it in LaTeX written as this:</p>
<p><br>
</p>
<p>(\hat{n} \cdot \nabla)(u \cdot \hat{n}) = 0 ?</p>
<p><br>
</p>
<p>If the wall normal is in the z-direction, then the open boundary condition for the velocity is:<br>
</p>
<p><br>
</p>
<p>d/dz u_z = 0?</p>
<p><br>
</p>
<p>Best regards,</p>
<p><br>
</p>
<p>Johan<br>
</p>
<p><br>
</p>
<p><br>
</p>
<br>
<br>
<div style="color:rgb(0,0,0)">
<hr tabindex="-1" style="display:inline-block; width:98%">
<div id="divRplyFwdMsg" dir="ltr"><font style="font-size:11pt" color="#000000" face="Calibri, sans-serif"><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>
<div> </div>
</div>
<div>
<div style="direction:ltr; font-family:Tahoma; color:#000000; font-size:10pt">
<div><br>
</div>
Dear Johan,
<div><br>
</div>
<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>
<div><br>
</div>
<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>
<div><br>
</div>
<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>
<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="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>
</font><br>
</div>
<div></div>
<div>
<div id="divtagdefaultwrapper" style="font-size:12pt; color:#000000; background-color:#FFFFFF; font-family:Calibri,Arial,Helvetica,sans-serif">
<p>Dear Neks,</p>
<p><br>
</p>
<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>
<p><br>
</p>
<p>grad(T) dot n = 0, where n is the normal to the boundary.</p>
<p><br>
</p>
<p>Since the heat flux is q = - grad(T), I would rather interpret this as a zero flux boundary condition.</p>
<p><br>
</p>
<p>And indeed, the insulated boundary described by equation (4.6) is identical to the open boundary condition.</p>
<p><br>
</p>
<p>Is equation (4.5) a type-O or is the open boundary for the temperature actually the same as an insulated boundary?</p>
<p><br>
</p>
<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>
</p>
<br>
<p>Best Regards,</p>
<p><br>
</p>
<p>Johan<br>
</p>
</div>
</div>
</div>
</div>
</div>
</div>
</div>
</div>
</div>
</div>
</div>
</div>
</div>
</div>
</div>
</body>
</html>