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Hi Ruth,<br>
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Thanks for your response. I have indeed worked around the problem by dividing the domain into 2 planes and doing two separate single progressions. I was still curious what the response would be because I would like understand how Bump works even if I can't
use it for this purpose.<br>
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I will look at the file you recommended I look at.<br>
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Thanks,<br>
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Nathan <br>
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Get <a href="https://aka.ms/ghei36">Outlook for Android</a></div>
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<div id="divRplyFwdMsg" dir="ltr"><font face="Calibri, sans-serif" color="#000000" style="font-size:11pt"><b>From:</b> Ruth Vazquez Sabariego <ruth.sabariego@kuleuven.be><br>
<b>Sent:</b> Wednesday, October 24, 2018 8:27:41 AM<br>
<b>To:</b> Nathan J. Neeteson<br>
<b>Cc:</b> gmsh@onelab.info<br>
<b>Subject:</b> Re: [Gmsh] Question about Progression and Bump</font>
<div> </div>
</div>
<div>Dear Nathan,
<div class=""><br class="">
</div>
<div class="">As you have noticed, the Bump does not do a double geometrical progression. </div>
<div class="">The formula used is a bit more complicated, you can see what it actually does in the code (meshGEdge.cpp).</div>
<div class=""><br class="">
</div>
<div class="">A double progression is not (yet?) available.</div>
<div class="">Work around by dividing your second region in two?</div>
<div class=""><br class="">
</div>
<div class="">Regards, </div>
<div class="">Ruth</div>
<div class=""><br class="">
</div>
<div class=""><br class="">
<div class="">
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<div class="" style="color:rgb(0,0,0); letter-spacing:normal; text-transform:none; white-space:normal; word-spacing:0px; orphans:auto; text-align:start; text-indent:0px; widows:auto; word-wrap:break-word">
—<br class="">
Prof. Ruth V. Sabariego<br class="">
KU Leuven <br class="">
Dept. Electrical Engineering ESAT/Electa, EnergyVille<br class="">
<a href="http://www.esat.kuleuven.be/electa" class="">http://www.esat.kuleuven.be/electa</a></div>
<div class="" style="orphans:auto; text-align:start; text-indent:0px; widows:auto; word-wrap:break-word">
<a href="http://www.energyville.be" class="">http://www.energyville.be</a></div>
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Free software: <a href="http://gmsh.info" class="">http://gmsh.info</a> | <a href="http://getdp.info" class="">http://getdp.info</a> | <a href="http://onelab.info" class="">http://onelab.info</a><br class="">
<br class="">
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</div>
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<div><br class="">
<blockquote type="cite" class="">
<div class="">On 23 Oct 2018, at 22:07, Nathan J. Neeteson <<a href="mailto:nneeteson@rglinc.com" class="">nneeteson@rglinc.com</a>> wrote:</div>
<br class="Apple-interchange-newline">
<div class="">
<div class="WordSection1" style="font-family:Helvetica; font-size:12px; font-style:normal; font-weight:normal; letter-spacing:normal; text-align:start; text-indent:0px; text-transform:none; white-space:normal; word-spacing:0px; text-decoration:none">
<div class="" style="margin:0cm 0cm 0.0001pt; font-size:11pt; font-family:Calibri,sans-serif">
Hello,</div>
<div class="" style="margin:0cm 0cm 0.0001pt; font-size:11pt; font-family:Calibri,sans-serif">
</div>
<div class="" style="margin:0cm 0cm 0.0001pt; font-size:11pt; font-family:Calibri,sans-serif">
I have a question about using Progression and Bump in neighboring blocks in a block-structured mesh. What I want is for the two blocks to have cells of the same height where they meet. I know the thickness of the first cell from the wall (dx0), the length of
each line (L), and the progression I want (r), so when I’m using Progression I can calculate the number of nodes to use as N = log(1+(L*(r-1))/(dx0)) / log(r) – 1. Then I can set the appropriate lines to Transfinite and assign them N Using Progression r and
it works as expected.</div>
<div class="" style="margin:0cm 0cm 0.0001pt; font-size:11pt; font-family:Calibri,sans-serif">
</div>
<div class="" style="margin:0cm 0cm 0.0001pt; font-size:11pt; font-family:Calibri,sans-serif">
However, in one of my blocks I want to refine towards both the top and bottom, so I need to use the Bump option. The problem is that I have no idea what “r” value to use after Bump (using the same r value as is used for Progression does not give me the results
I want) and I also have no idea how to calculate the number of points to use along this line. MY first instinct was to calculate the number of points needed as double the number of points for a single progression with half of the length (two progressions end
to end). I think this is right, but when I use r after Bump I get no refinement. What value am I supposed to use for number of points and the rate of growth when using the Bump function so that I get the equivalent of the product of two Progressions end to
end?</div>
<div class="" style="margin:0cm 0cm 0.0001pt; font-size:11pt; font-family:Calibri,sans-serif">
</div>
<div class="" style="margin:0cm 0cm 0.0001pt; font-size:11pt; font-family:Calibri,sans-serif">
Here is a zoomed in look at where I want the first cells to match heights:</div>
<div class="" style="margin:0cm 0cm 0.0001pt; font-size:11pt; font-family:Calibri,sans-serif">
</div>
<div class="" style="margin:0cm 0cm 0.0001pt; font-size:11pt; font-family:Calibri,sans-serif">
The bottom block uses single progression and the upper block you are seeing the lower end of the double progression.</div>
<div class="" style="margin:0cm 0cm 0.0001pt; font-size:11pt; font-family:Calibri,sans-serif">
<span class=""><span id="cid:image001.png@01D46AD9.B5964A40"><image001.png></span></span></div>
<div class="" style="margin:0cm 0cm 0.0001pt; font-size:11pt; font-family:Calibri,sans-serif">
</div>
<div class="" style="margin:0cm 0cm 0.0001pt; font-size:11pt; font-family:Calibri,sans-serif">
Here is my .geo file:</div>
<div class="" style="margin:0cm 0cm 0.0001pt; font-size:11pt; font-family:Calibri,sans-serif">
-------------------------------------------------------------------------------------------</div>
<div class="" style="margin:0cm 0cm 0.0001pt 36pt; font-size:11pt; font-family:Calibri,sans-serif">
<span class="" style="font-family:Arial,sans-serif">// orifice properties</span></div>
<div class="" style="margin:0cm 0cm 0.0001pt 36pt; font-size:11pt; font-family:Calibri,sans-serif">
<span class="" style="font-family:Arial,sans-serif">orificeLength = 0.03;</span></div>
<div class="" style="margin:0cm 0cm 0.0001pt 36pt; font-size:11pt; font-family:Calibri,sans-serif">
<span class="" style="font-family:Arial,sans-serif">orificeRadius = 0.002;</span></div>
<div class="" style="margin:0cm 0cm 0.0001pt 36pt; font-size:11pt; font-family:Calibri,sans-serif">
<span class="" style="font-family:Arial,sans-serif"> </span></div>
<div class="" style="margin:0cm 0cm 0.0001pt 36pt; font-size:11pt; font-family:Calibri,sans-serif">
<span class="" style="font-family:Arial,sans-serif">// pipe properties</span></div>
<div class="" style="margin:0cm 0cm 0.0001pt 36pt; font-size:11pt; font-family:Calibri,sans-serif">
<span class="" style="font-family:Arial,sans-serif">pipeRadius = 0.05;</span></div>
<div class="" style="margin:0cm 0cm 0.0001pt 36pt; font-size:11pt; font-family:Calibri,sans-serif">
<span class="" style="font-family:Arial,sans-serif"> </span></div>
<div class="" style="margin:0cm 0cm 0.0001pt 36pt; font-size:11pt; font-family:Calibri,sans-serif">
<span class="" style="font-family:Arial,sans-serif">// distance from orifice to inlet</span></div>
<div class="" style="margin:0cm 0cm 0.0001pt 36pt; font-size:11pt; font-family:Calibri,sans-serif">
<span class="" style="font-family:Arial,sans-serif">inletDist = 5*pipeRadius;</span></div>
<div class="" style="margin:0cm 0cm 0.0001pt 36pt; font-size:11pt; font-family:Calibri,sans-serif">
<span class="" style="font-family:Arial,sans-serif"> </span></div>
<div class="" style="margin:0cm 0cm 0.0001pt 36pt; font-size:11pt; font-family:Calibri,sans-serif">
<span class="" style="font-family:Arial,sans-serif">// distance from orifice to outlet</span></div>
<div class="" style="margin:0cm 0cm 0.0001pt 36pt; font-size:11pt; font-family:Calibri,sans-serif">
<span class="" style="font-family:Arial,sans-serif">outletDist = 5*pipeRadius;</span></div>
<div class="" style="margin:0cm 0cm 0.0001pt 36pt; font-size:11pt; font-family:Calibri,sans-serif">
<span class="" style="font-family:Arial,sans-serif"> </span></div>
<div class="" style="margin:0cm 0cm 0.0001pt 36pt; font-size:11pt; font-family:Calibri,sans-serif">
<span class="" style="font-family:Arial,sans-serif">// grid size parameters</span></div>
<div class="" style="margin:0cm 0cm 0.0001pt 36pt; font-size:11pt; font-family:Calibri,sans-serif">
<span class="" style="font-family:Arial,sans-serif">r = 1.1; // growth parameter</span></div>
<div class="" style="margin:0cm 0cm 0.0001pt 36pt; font-size:11pt; font-family:Calibri,sans-serif">
<span class="" style="font-family:Arial,sans-serif">dx0 = 1*10^(-4); // first wall dist for y+=1</span></div>
<div class="" style="margin:0cm 0cm 0.0001pt 36pt; font-size:11pt; font-family:Calibri,sans-serif">
<span class="" style="font-family:Arial,sans-serif"> </span></div>
<div class="" style="margin:0cm 0cm 0.0001pt 36pt; font-size:11pt; font-family:Calibri,sans-serif">
<span class="" style="font-family:Arial,sans-serif">upstreamNx = (Log(1 + ((inletDist*(r-1))/(dx0))) / Log(r)) - 1; // number of elements in x direction upstream</span></div>
<div class="" style="margin:0cm 0cm 0.0001pt 36pt; font-size:11pt; font-family:Calibri,sans-serif">
<span class="" style="font-family:Arial,sans-serif">downstreamNx = (Log(1 + ((outletDist*(r-1))/(dx0))) / Log(r)) - 1; // number of elements in x direction upstream</span></div>
<div class="" style="margin:0cm 0cm 0.0001pt 36pt; font-size:11pt; font-family:Calibri,sans-serif">
<span class="" style="font-family:Arial,sans-serif">orificeNx = orificeLength/dx0; // number of elements in x direction inside orifice</span></div>
<div class="" style="margin:0cm 0cm 0.0001pt 36pt; font-size:11pt; font-family:Calibri,sans-serif">
<span class="" style="font-family:Arial,sans-serif"> </span></div>
<div class="" style="margin:0cm 0cm 0.0001pt 36pt; font-size:11pt; font-family:Calibri,sans-serif">
<span class="" style="font-family:Arial,sans-serif">upstreamOrificeNy = orificeRadius/dx0;</span></div>
<div class="" style="margin:0cm 0cm 0.0001pt 36pt; font-size:11pt; font-family:Calibri,sans-serif">
<span class="" style="font-family:Arial,sans-serif">upstreamPipeNy = 2*((Log(1 + ((((pipeRadius-orificeRadius)/2)*(r-1))/(dx0))) / Log(r)) - 1);</span></div>
<div class="" style="margin:0cm 0cm 0.0001pt 36pt; font-size:11pt; font-family:Calibri,sans-serif">
<span class="" style="font-family:Arial,sans-serif"> </span></div>
<div class="" style="margin:0cm 0cm 0.0001pt 36pt; font-size:11pt; font-family:Calibri,sans-serif">
<span class="" style="font-family:Arial,sans-serif"> </span></div>
<div class="" style="margin:0cm 0cm 0.0001pt 36pt; font-size:11pt; font-family:Calibri,sans-serif">
<span class="" style="font-family:Arial,sans-serif">// element index</span></div>
<div class="" style="margin:0cm 0cm 0.0001pt 36pt; font-size:11pt; font-family:Calibri,sans-serif">
<span class="" style="font-family:Arial,sans-serif">i = 1;</span></div>
<div class="" style="margin:0cm 0cm 0.0001pt 36pt; font-size:11pt; font-family:Calibri,sans-serif">
<span class="" style="font-family:Arial,sans-serif"> </span></div>
<div class="" style="margin:0cm 0cm 0.0001pt 36pt; font-size:11pt; font-family:Calibri,sans-serif">
<span class="" style="font-family:Arial,sans-serif">// ~~-------------------------~~ POINTS ~~-------------------------~~</span></div>
<div class="" style="margin:0cm 0cm 0.0001pt 36pt; font-size:11pt; font-family:Calibri,sans-serif">
<span class="" style="font-family:Arial,sans-serif">// order of point definition doesn't matter, just give descriptive names</span></div>
<div class="" style="margin:0cm 0cm 0.0001pt 36pt; font-size:11pt; font-family:Calibri,sans-serif">
<span class="" style="font-family:Arial,sans-serif"> </span></div>
<div class="" style="margin:0cm 0cm 0.0001pt 36pt; font-size:11pt; font-family:Calibri,sans-serif">
<span class="" style="font-family:Arial,sans-serif">inletCenterPoint = i;</span></div>
<div class="" style="margin:0cm 0cm 0.0001pt 36pt; font-size:11pt; font-family:Calibri,sans-serif">
<span class="" style="font-family:Arial,sans-serif">Point(i) = {-orificeLength-inletDist,0,0,1};</span></div>
<div class="" style="margin:0cm 0cm 0.0001pt 36pt; font-size:11pt; font-family:Calibri,sans-serif">
<span class="" style="font-family:Arial,sans-serif">i=i+1;</span></div>
<div class="" style="margin:0cm 0cm 0.0001pt 36pt; font-size:11pt; font-family:Calibri,sans-serif">
<span class="" style="font-family:Arial,sans-serif"> </span></div>
<div class="" style="margin:0cm 0cm 0.0001pt 36pt; font-size:11pt; font-family:Calibri,sans-serif">
<span class="" style="font-family:Arial,sans-serif">inletPipeWallPoint = i;</span></div>
<div class="" style="margin:0cm 0cm 0.0001pt 36pt; font-size:11pt; font-family:Calibri,sans-serif">
<span class="" style="font-family:Arial,sans-serif">Point(i) = {-orificeLength-inletDist,pipeRadius,0,1};</span></div>
<div class="" style="margin:0cm 0cm 0.0001pt 36pt; font-size:11pt; font-family:Calibri,sans-serif">
<span class="" style="font-family:Arial,sans-serif">i=i+1;</span></div>
<div class="" style="margin:0cm 0cm 0.0001pt 36pt; font-size:11pt; font-family:Calibri,sans-serif">
<span class="" style="font-family:Arial,sans-serif"> </span></div>
<div class="" style="margin:0cm 0cm 0.0001pt 36pt; font-size:11pt; font-family:Calibri,sans-serif">
<span class="" style="font-family:Arial,sans-serif">inletOrificeWallPoint = i;</span></div>
<div class="" style="margin:0cm 0cm 0.0001pt 36pt; font-size:11pt; font-family:Calibri,sans-serif">
<span class="" style="font-family:Arial,sans-serif">Point(i) = {-orificeLength-inletDist,orificeRadius,0,1};</span></div>
<div class="" style="margin:0cm 0cm 0.0001pt 36pt; font-size:11pt; font-family:Calibri,sans-serif">
<span class="" style="font-family:Arial,sans-serif">i=i+1;</span></div>
<div class="" style="margin:0cm 0cm 0.0001pt 36pt; font-size:11pt; font-family:Calibri,sans-serif">
<span class="" style="font-family:Arial,sans-serif"> </span></div>
<div class="" style="margin:0cm 0cm 0.0001pt 36pt; font-size:11pt; font-family:Calibri,sans-serif">
<span class="" style="font-family:Arial,sans-serif">upOrificeCenterPoint = i;</span></div>
<div class="" style="margin:0cm 0cm 0.0001pt 36pt; font-size:11pt; font-family:Calibri,sans-serif">
<span class="" style="font-family:Arial,sans-serif">Point(i) = {-orificeLength,0,0,1};</span></div>
<div class="" style="margin:0cm 0cm 0.0001pt 36pt; font-size:11pt; font-family:Calibri,sans-serif">
<span class="" style="font-family:Arial,sans-serif">i=i+1;</span></div>
<div class="" style="margin:0cm 0cm 0.0001pt 36pt; font-size:11pt; font-family:Calibri,sans-serif">
<span class="" style="font-family:Arial,sans-serif"> </span></div>
<div class="" style="margin:0cm 0cm 0.0001pt 36pt; font-size:11pt; font-family:Calibri,sans-serif">
<span class="" style="font-family:Arial,sans-serif">upOrificePipeWallPoint = i;</span></div>
<div class="" style="margin:0cm 0cm 0.0001pt 36pt; font-size:11pt; font-family:Calibri,sans-serif">
<span class="" style="font-family:Arial,sans-serif">Point(i) = {-orificeLength,pipeRadius,0,1};</span></div>
<div class="" style="margin:0cm 0cm 0.0001pt 36pt; font-size:11pt; font-family:Calibri,sans-serif">
<span class="" style="font-family:Arial,sans-serif">i=i+1;</span></div>
<div class="" style="margin:0cm 0cm 0.0001pt 36pt; font-size:11pt; font-family:Calibri,sans-serif">
<span class="" style="font-family:Arial,sans-serif"> </span></div>
<div class="" style="margin:0cm 0cm 0.0001pt 36pt; font-size:11pt; font-family:Calibri,sans-serif">
<span class="" style="font-family:Arial,sans-serif">upOrificeOrificeWallPoint = i;</span></div>
<div class="" style="margin:0cm 0cm 0.0001pt 36pt; font-size:11pt; font-family:Calibri,sans-serif">
<span class="" style="font-family:Arial,sans-serif">Point(i) = {-orificeLength,orificeRadius,0,1};</span></div>
<div class="" style="margin:0cm 0cm 0.0001pt 36pt; font-size:11pt; font-family:Calibri,sans-serif">
<span class="" style="font-family:Arial,sans-serif">i=i+1;</span></div>
<div class="" style="margin:0cm 0cm 0.0001pt 36pt; font-size:11pt; font-family:Calibri,sans-serif">
<span class="" style="font-family:Arial,sans-serif"> </span></div>
<div class="" style="margin:0cm 0cm 0.0001pt 36pt; font-size:11pt; font-family:Calibri,sans-serif">
<span class="" style="font-family:Arial,sans-serif"> </span></div>
<div class="" style="margin:0cm 0cm 0.0001pt 36pt; font-size:11pt; font-family:Calibri,sans-serif">
<span class="" style="font-family:Arial,sans-serif">// ~~-------------------------~~ LINES ~~-------------------------~~</span></div>
<div class="" style="margin:0cm 0cm 0.0001pt 36pt; font-size:11pt; font-family:Calibri,sans-serif">
<span class="" style="font-family:Arial,sans-serif">// all lines should be defined going up and/or to the right for consistency</span></div>
<div class="" style="margin:0cm 0cm 0.0001pt 36pt; font-size:11pt; font-family:Calibri,sans-serif">
<span class="" style="font-family:Arial,sans-serif"> </span></div>
<div class="" style="margin:0cm 0cm 0.0001pt 36pt; font-size:11pt; font-family:Calibri,sans-serif">
<span class="" style="font-family:Arial,sans-serif">inletOrificeLine = i;</span></div>
<div class="" style="margin:0cm 0cm 0.0001pt 36pt; font-size:11pt; font-family:Calibri,sans-serif">
<span class="" style="font-family:Arial,sans-serif">Line(i) = {inletCenterPoint,inletOrificeWallPoint};</span></div>
<div class="" style="margin:0cm 0cm 0.0001pt 36pt; font-size:11pt; font-family:Calibri,sans-serif">
<span class="" style="font-family:Arial,sans-serif">i=i+1;</span></div>
<div class="" style="margin:0cm 0cm 0.0001pt 36pt; font-size:11pt; font-family:Calibri,sans-serif">
<span class="" style="font-family:Arial,sans-serif"> </span></div>
<div class="" style="margin:0cm 0cm 0.0001pt 36pt; font-size:11pt; font-family:Calibri,sans-serif">
<span class="" style="font-family:Arial,sans-serif">inletPipeLine = i;</span></div>
<div class="" style="margin:0cm 0cm 0.0001pt 36pt; font-size:11pt; font-family:Calibri,sans-serif">
<span class="" style="font-family:Arial,sans-serif">Line(i) = {inletOrificeWallPoint,inletPipeWallPoint};</span></div>
<div class="" style="margin:0cm 0cm 0.0001pt 36pt; font-size:11pt; font-family:Calibri,sans-serif">
<span class="" style="font-family:Arial,sans-serif">i=i+1;</span></div>
<div class="" style="margin:0cm 0cm 0.0001pt 36pt; font-size:11pt; font-family:Calibri,sans-serif">
<span class="" style="font-family:Arial,sans-serif"> </span></div>
<div class="" style="margin:0cm 0cm 0.0001pt 36pt; font-size:11pt; font-family:Calibri,sans-serif">
<span class="" style="font-family:Arial,sans-serif">upstreamPipeWallLine = i;</span></div>
<div class="" style="margin:0cm 0cm 0.0001pt 36pt; font-size:11pt; font-family:Calibri,sans-serif">
<span class="" style="font-family:Arial,sans-serif">Line(i) = {inletPipeWallPoint,upOrificePipeWallPoint};</span></div>
<div class="" style="margin:0cm 0cm 0.0001pt 36pt; font-size:11pt; font-family:Calibri,sans-serif">
<span class="" style="font-family:Arial,sans-serif">i=i+1;</span></div>
<div class="" style="margin:0cm 0cm 0.0001pt 36pt; font-size:11pt; font-family:Calibri,sans-serif">
<span class="" style="font-family:Arial,sans-serif"> </span></div>
<div class="" style="margin:0cm 0cm 0.0001pt 36pt; font-size:11pt; font-family:Calibri,sans-serif">
<span class="" style="font-family:Arial,sans-serif">upstreamCenterLine = i;</span></div>
<div class="" style="margin:0cm 0cm 0.0001pt 36pt; font-size:11pt; font-family:Calibri,sans-serif">
<span class="" style="font-family:Arial,sans-serif">Line(i) = {inletCenterPoint,upOrificeCenterPoint};</span></div>
<div class="" style="margin:0cm 0cm 0.0001pt 36pt; font-size:11pt; font-family:Calibri,sans-serif">
<span class="" style="font-family:Arial,sans-serif">i=i+1;</span></div>
<div class="" style="margin:0cm 0cm 0.0001pt 36pt; font-size:11pt; font-family:Calibri,sans-serif">
<span class="" style="font-family:Arial,sans-serif"> </span></div>
<div class="" style="margin:0cm 0cm 0.0001pt 36pt; font-size:11pt; font-family:Calibri,sans-serif">
<span class="" style="font-family:Arial,sans-serif">upstreamOrificeLine = i;</span></div>
<div class="" style="margin:0cm 0cm 0.0001pt 36pt; font-size:11pt; font-family:Calibri,sans-serif">
<span class="" style="font-family:Arial,sans-serif">Line(i) = {inletOrificeWallPoint,upOrificeOrificeWallPoint};</span></div>
<div class="" style="margin:0cm 0cm 0.0001pt 36pt; font-size:11pt; font-family:Calibri,sans-serif">
<span class="" style="font-family:Arial,sans-serif">i=i+1;</span></div>
<div class="" style="margin:0cm 0cm 0.0001pt 36pt; font-size:11pt; font-family:Calibri,sans-serif">
<span class="" style="font-family:Arial,sans-serif"> </span></div>
<div class="" style="margin:0cm 0cm 0.0001pt 36pt; font-size:11pt; font-family:Calibri,sans-serif">
<span class="" style="font-family:Arial,sans-serif">upstreamOrificePlateLine = i;</span></div>
<div class="" style="margin:0cm 0cm 0.0001pt 36pt; font-size:11pt; font-family:Calibri,sans-serif">
<span class="" style="font-family:Arial,sans-serif">Line(i) = {upOrificeOrificeWallPoint,upOrificePipeWallPoint};</span></div>
<div class="" style="margin:0cm 0cm 0.0001pt 36pt; font-size:11pt; font-family:Calibri,sans-serif">
<span class="" style="font-family:Arial,sans-serif">i=i+1;</span></div>
<div class="" style="margin:0cm 0cm 0.0001pt 36pt; font-size:11pt; font-family:Calibri,sans-serif">
<span class="" style="font-family:Arial,sans-serif"> </span></div>
<div class="" style="margin:0cm 0cm 0.0001pt 36pt; font-size:11pt; font-family:Calibri,sans-serif">
<span class="" style="font-family:Arial,sans-serif">upstreamOrificeEntryLine = i;</span></div>
<div class="" style="margin:0cm 0cm 0.0001pt 36pt; font-size:11pt; font-family:Calibri,sans-serif">
<span class="" style="font-family:Arial,sans-serif">Line(i) = {upOrificeCenterPoint,upOrificeOrificeWallPoint};</span></div>
<div class="" style="margin:0cm 0cm 0.0001pt 36pt; font-size:11pt; font-family:Calibri,sans-serif">
<span class="" style="font-family:Arial,sans-serif">i=i+1;</span></div>
<div class="" style="margin:0cm 0cm 0.0001pt 36pt; font-size:11pt; font-family:Calibri,sans-serif">
<span class="" style="font-family:Arial,sans-serif"> </span></div>
<div class="" style="margin:0cm 0cm 0.0001pt 36pt; font-size:11pt; font-family:Calibri,sans-serif">
<span class="" style="font-family:Arial,sans-serif">// ~~-------------------------~~ LINE LOOPS ~~-------------------------~~</span></div>
<div class="" style="margin:0cm 0cm 0.0001pt 36pt; font-size:11pt; font-family:Calibri,sans-serif">
<span class="" style="font-family:Arial,sans-serif">// all line loops should be oriented clockwise</span></div>
<div class="" style="margin:0cm 0cm 0.0001pt 36pt; font-size:11pt; font-family:Calibri,sans-serif">
<span class="" style="font-family:Arial,sans-serif"> </span></div>
<div class="" style="margin:0cm 0cm 0.0001pt 36pt; font-size:11pt; font-family:Calibri,sans-serif">
<span class="" style="font-family:Arial,sans-serif">upstreamPipeLoop = i;</span></div>
<div class="" style="margin:0cm 0cm 0.0001pt 36pt; font-size:11pt; font-family:Calibri,sans-serif">
<span class="" style="font-family:Arial,sans-serif">Line Loop(i) = {inletPipeLine,upstreamPipeWallLine,-upstreamOrificePlateLine,-upstreamOrificeLine};</span></div>
<div class="" style="margin:0cm 0cm 0.0001pt 36pt; font-size:11pt; font-family:Calibri,sans-serif">
<span class="" style="font-family:Arial,sans-serif">i=i+1;</span></div>
<div class="" style="margin:0cm 0cm 0.0001pt 36pt; font-size:11pt; font-family:Calibri,sans-serif">
<span class="" style="font-family:Arial,sans-serif"> </span></div>
<div class="" style="margin:0cm 0cm 0.0001pt 36pt; font-size:11pt; font-family:Calibri,sans-serif">
<span class="" style="font-family:Arial,sans-serif">upstreamOrificeLoop = i;</span></div>
<div class="" style="margin:0cm 0cm 0.0001pt 36pt; font-size:11pt; font-family:Calibri,sans-serif">
<span class="" style="font-family:Arial,sans-serif">Line Loop(i) = {inletOrificeLine,upstreamOrificeLine,-upstreamOrificeEntryLine,-upstreamCenterLine};</span></div>
<div class="" style="margin:0cm 0cm 0.0001pt 36pt; font-size:11pt; font-family:Calibri,sans-serif">
<span class="" style="font-family:Arial,sans-serif">i=i+1;</span></div>
<div class="" style="margin:0cm 0cm 0.0001pt 36pt; font-size:11pt; font-family:Calibri,sans-serif">
<span class="" style="font-family:Arial,sans-serif"> </span></div>
<div class="" style="margin:0cm 0cm 0.0001pt 36pt; font-size:11pt; font-family:Calibri,sans-serif">
<span class="" style="font-family:Arial,sans-serif"> </span></div>
<div class="" style="margin:0cm 0cm 0.0001pt 36pt; font-size:11pt; font-family:Calibri,sans-serif">
<span class="" style="font-family:Arial,sans-serif"> </span></div>
<div class="" style="margin:0cm 0cm 0.0001pt 36pt; font-size:11pt; font-family:Calibri,sans-serif">
<span class="" style="font-family:Arial,sans-serif">// ~~-------------------------~~ PLANE SURFACES ~~-------------------------~~</span></div>
<div class="" style="margin:0cm 0cm 0.0001pt 36pt; font-size:11pt; font-family:Calibri,sans-serif">
<span class="" style="font-family:Arial,sans-serif"> </span></div>
<div class="" style="margin:0cm 0cm 0.0001pt 36pt; font-size:11pt; font-family:Calibri,sans-serif">
<span class="" style="font-family:Arial,sans-serif">upstreamPipePlane = i;</span></div>
<div class="" style="margin:0cm 0cm 0.0001pt 36pt; font-size:11pt; font-family:Calibri,sans-serif">
<span class="" style="font-family:Arial,sans-serif">Plane Surface(i) = upstreamPipeLoop;</span></div>
<div class="" style="margin:0cm 0cm 0.0001pt 36pt; font-size:11pt; font-family:Calibri,sans-serif">
<span class="" style="font-family:Arial,sans-serif">i=i+1;</span></div>
<div class="" style="margin:0cm 0cm 0.0001pt 36pt; font-size:11pt; font-family:Calibri,sans-serif">
<span class="" style="font-family:Arial,sans-serif"> </span></div>
<div class="" style="margin:0cm 0cm 0.0001pt 36pt; font-size:11pt; font-family:Calibri,sans-serif">
<span class="" style="font-family:Arial,sans-serif">upstreamOrificePlane = i;</span></div>
<div class="" style="margin:0cm 0cm 0.0001pt 36pt; font-size:11pt; font-family:Calibri,sans-serif">
<span class="" style="font-family:Arial,sans-serif">Plane Surface(i) = upstreamOrificeLoop;</span></div>
<div class="" style="margin:0cm 0cm 0.0001pt 36pt; font-size:11pt; font-family:Calibri,sans-serif">
<span class="" style="font-family:Arial,sans-serif">i=i+1;</span></div>
<div class="" style="margin:0cm 0cm 0.0001pt 36pt; font-size:11pt; font-family:Calibri,sans-serif">
<span class="" style="font-family:Arial,sans-serif"> </span></div>
<div class="" style="margin:0cm 0cm 0.0001pt 36pt; font-size:11pt; font-family:Calibri,sans-serif">
<span class="" style="font-family:Arial,sans-serif"> </span></div>
<div class="" style="margin:0cm 0cm 0.0001pt 36pt; font-size:11pt; font-family:Calibri,sans-serif">
<span class="" style="font-family:Arial,sans-serif"> </span></div>
<div class="" style="margin:0cm 0cm 0.0001pt 36pt; font-size:11pt; font-family:Calibri,sans-serif">
<span class="" style="font-family:Arial,sans-serif">// ~~-------------------------~~ MAKE STRUCTURED ~~-------------------------~~</span></div>
<div class="" style="margin:0cm 0cm 0.0001pt 36pt; font-size:11pt; font-family:Calibri,sans-serif">
<span class="" style="font-family:Arial,sans-serif"> </span></div>
<div class="" style="margin:0cm 0cm 0.0001pt 36pt; font-size:11pt; font-family:Calibri,sans-serif">
<span class="" style="font-family:Arial,sans-serif">// the x-oriented lines upstream of the orifice</span></div>
<div class="" style="margin:0cm 0cm 0.0001pt 36pt; font-size:11pt; font-family:Calibri,sans-serif">
<span class="" style="font-family:Arial,sans-serif">Transfinite Line{-upstreamCenterLine,-upstreamOrificeLine,-upstreamPipeWallLine} = upstreamNx Using Progression r;</span></div>
<div class="" style="margin:0cm 0cm 0.0001pt 36pt; font-size:11pt; font-family:Calibri,sans-serif">
<span class="" style="font-family:Arial,sans-serif"> </span></div>
<div class="" style="margin:0cm 0cm 0.0001pt 36pt; font-size:11pt; font-family:Calibri,sans-serif">
<span class="" style="font-family:Arial,sans-serif">// the x-oriented lines in the orifice</span></div>
<div class="" style="margin:0cm 0cm 0.0001pt 36pt; font-size:11pt; font-family:Calibri,sans-serif">
<span class="" style="font-family:Arial,sans-serif"> </span></div>
<div class="" style="margin:0cm 0cm 0.0001pt 36pt; font-size:11pt; font-family:Calibri,sans-serif">
<span class="" style="font-family:Arial,sans-serif"> </span></div>
<div class="" style="margin:0cm 0cm 0.0001pt 36pt; font-size:11pt; font-family:Calibri,sans-serif">
<span class="" style="font-family:Arial,sans-serif">// the x-oriented lines downstream of the orifice</span></div>
<div class="" style="margin:0cm 0cm 0.0001pt 36pt; font-size:11pt; font-family:Calibri,sans-serif">
<span class="" style="font-family:Arial,sans-serif"> </span></div>
<div class="" style="margin:0cm 0cm 0.0001pt 36pt; font-size:11pt; font-family:Calibri,sans-serif">
<span class="" style="font-family:Arial,sans-serif"> </span></div>
<div class="" style="margin:0cm 0cm 0.0001pt 36pt; font-size:11pt; font-family:Calibri,sans-serif">
<span class="" style="font-family:Arial,sans-serif">// the y-oriented lines from the centerline to the orifice radius</span></div>
<div class="" style="margin:0cm 0cm 0.0001pt 36pt; font-size:11pt; font-family:Calibri,sans-serif">
<span class="" style="font-family:Arial,sans-serif">Transfinite Line{inletOrificeLine,upstreamOrificeEntryLine} = upstreamOrificeNy;</span></div>
<div class="" style="margin:0cm 0cm 0.0001pt 36pt; font-size:11pt; font-family:Calibri,sans-serif">
<span class="" style="font-family:Arial,sans-serif"> </span></div>
<div class="" style="margin:0cm 0cm 0.0001pt 36pt; font-size:11pt; font-family:Calibri,sans-serif">
<span class="" style="font-family:Arial,sans-serif">// the y-oriented lines from the orifice radius to the pipe radius</span></div>
<div class="" style="margin:0cm 0cm 0.0001pt 36pt; font-size:11pt; font-family:Calibri,sans-serif">
<span class="" style="font-family:Arial,sans-serif">Transfinite Line{inletPipeLine,upstreamOrificePlateLine} = upstreamPipeNy Using Bump 0.05;</span></div>
<div class="" style="margin:0cm 0cm 0.0001pt 36pt; font-size:11pt; font-family:Calibri,sans-serif">
<span class="" style="font-family:Arial,sans-serif"> </span></div>
<div class="" style="margin:0cm 0cm 0.0001pt 36pt; font-size:11pt; font-family:Calibri,sans-serif">
<span class="" style="font-family:Arial,sans-serif"> </span></div>
<div class="" style="margin:0cm 0cm 0.0001pt 36pt; font-size:11pt; font-family:Calibri,sans-serif">
<span class="" style="font-family:Arial,sans-serif"> </span></div>
<div class="" style="margin:0cm 0cm 0.0001pt 36pt; font-size:11pt; font-family:Calibri,sans-serif">
<span class="" style="font-family:Arial,sans-serif">Transfinite Surface{upstreamOrificePlane};</span></div>
<div class="" style="margin:0cm 0cm 0.0001pt 36pt; font-size:11pt; font-family:Calibri,sans-serif">
<span class="" style="font-family:Arial,sans-serif">Recombine Surface{upstreamOrificePlane};</span></div>
<div class="" style="margin:0cm 0cm 0.0001pt 36pt; font-size:11pt; font-family:Calibri,sans-serif">
<span class="" style="font-family:Arial,sans-serif"> </span></div>
<div class="" style="margin:0cm 0cm 0.0001pt 36pt; font-size:11pt; font-family:Calibri,sans-serif">
<span class="" style="font-family:Arial,sans-serif">Transfinite Surface{upstreamPipePlane};</span></div>
<div class="" style="margin:0cm 0cm 0.0001pt 36pt; font-size:11pt; font-family:Calibri,sans-serif">
<span class="" style="font-family:Arial,sans-serif">Recombine Surface{upstreamPipePlane};</span></div>
<div class="" style="margin:0cm 0cm 0.0001pt; font-size:11pt; font-family:Calibri,sans-serif">
-------------------------------------------------------------------------------------------</div>
<div class="" style="margin:0cm 0cm 0.0001pt; font-size:11pt; font-family:Calibri,sans-serif">
</div>
<div class="" style="margin:0cm 0cm 0.0001pt; font-size:11pt; font-family:Calibri,sans-serif">
Thanks,</div>
<div class="" style="margin:0cm 0cm 0.0001pt; font-size:11pt; font-family:Calibri,sans-serif">
</div>
<div class="" style="margin:0cm 0cm 0.0001pt; font-size:11pt; font-family:Calibri,sans-serif">
<span lang="EN-US" class="">Nathan J. Neeteson, M.Sc.</span></div>
<div class="" style="margin:0cm 0cm 0.0001pt; font-size:11pt; font-family:Calibri,sans-serif">
<span lang="EN-US" class="">Flow Control Research Engineer</span></div>
<div class="" style="margin:0cm 0cm 0.0001pt; font-size:11pt; font-family:Calibri,sans-serif">
<b class=""><span lang="EN-US" class="">RGL Reservoir Management Inc.</span></b></div>
<div class="" style="margin:0cm 0cm 0.0001pt; font-size:11pt; font-family:Calibri,sans-serif">
<span lang="EN-US" class="">Engineering & Design Group</span></div>
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