"$xgradualdiv" 修訂間的差異

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(未顯示由 2 位使用者於中間所作的 2 次修訂)
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: Example
 
: Example
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$xnode
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0.0
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20.0
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40.0
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60.0
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$xdiv
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30
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70
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80
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$xgradualdiv
 
$xgradualdiv
0 1
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0
 
1 1.1
 
1 1.1
1 1.1
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2 0.95
2 1.1
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2 1.1
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<br>'''<big><big>The $xgradualdiv setting in GUI interface is here</big></big>''' <br>
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1. After setting up the X-nodes, press '''Edit the nodes'''.<br>
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2. Choose the 1<sup>st</sup> node and set the Method to '''Uniform''' with a Mesh ratio of 0.00.<br>
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[[檔案:2D_xgradualdiv_fig1.jpg|1200px]]<br><br>
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3. Choose the 2<sup>nd</sup> node and set the Method to '''Gradual change''' with a Mesh ratio of 1.10.<br>
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[[檔案:2D_xgradualdiv_fig2.jpg|1200px]]<br><br>
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4. Choose the 3<sup>rd</sup> node and set the Method to '''Bump''' with a Mesh ratio of 0.95.<br>
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[[檔案:2D_xgradualdiv_fig3.jpg|1200px]]<br><br>
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[[檔案:2D_xgradualdiv_fig4.jpg|1200px]]
   
 
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: Related commands
 
: Related commands
:; [[$ygradualdiv]]
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:; [[$ygradualdiv]] , [[$xnode]],[[$xdiv]]

於 2024年10月21日 (一) 17:38 的最新修訂

This function is to determine how the segment is divided. There are two columns to fill in. The first column i should be filled in an integer 0, 1, or 2.

i = 0: Uniform. This means the segment is divided equally with the same spacing.
i = 1: Gradual. This means the segment is divided whether from small spacing to large spacing or in the opposite way. The spacing is distributed like a geometric progression
i = 2: Bump. This means the segment can be divided into two forms small-large-small or large-small-large.

The second column r should be filled in a real number.
Mesh2.png

If r < 1 If r = 1 If r > 1
Uniform (0) uniform uniform uniform
Gradual (1) large -> small uniform small -> large
Bump (2) large -> small -> large uniform small -> large -> small


If the total layer thickness is l  and i=1, then if the smallest separation distance is a 
l = a+ar+ar^{2}+ar^{3}+ar^{4}+...+ar^{N} 
where N is the total grid number defined in $xdiv
Then   l = a\frac{r^{N}-1}{r-1} 


If the total layer thickness is l  and i=2, then if the smallest separation distance is a 
l/2 = a+ar+ar^{2}+ar^{3}+ar^{4}+...+ar^{N/2} 
where N is the total grid number defined in $ydiv
Then   l = 2 \cdot a\frac{r^{N/2}-1}{r-1} 


Example
$xnode
0.0
20.0
40.0
60.0

$xdiv
30 
70 
80

$xgradualdiv
0 
1 1.1
2 0.95


The $xgradualdiv setting in GUI interface is here
1. After setting up the X-nodes, press Edit the nodes.
2. Choose the 1st node and set the Method to Uniform with a Mesh ratio of 0.00.
2D xgradualdiv fig1.jpg

3. Choose the 2nd node and set the Method to Gradual change with a Mesh ratio of 1.10.
2D xgradualdiv fig2.jpg

4. Choose the 3rd node and set the Method to Bump with a Mesh ratio of 0.95.
2D xgradualdiv fig3.jpg

2D xgradualdiv fig4.jpg



Related commands
$ygradualdiv , $xnode,$xdiv