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Block Mesh Simplegrading Question

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Old   February 14, 2014, 10:47
Lightbulb Block Mesh Simplegrading Question
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Euan Foster
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Dear all,

Currently, I have a complicated blockMesh in that I have specified all elements to be the same length. However this seems very inefficient computationally and I was wondering if anyone could help me out with the simplegrading algorithm.

There are sudden expansions and contractions in my mesh and I want the elements to decrease in size where these two sections meet.

Is there any equations out there online or any theory based on the length in an axis so I could input a simplegrading number and achieve a specified element length at the end?

I appreciate any help I get.

Kind regards,

Euan Foster.
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Old   February 14, 2014, 11:27
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Gerhard Holzinger
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The number you enter for grading is the expansion ratio e - the ratio of the length of the last cell and the length of the first cell.

e = d_n / d_1 -- > d_1 = e * d_n

Now we define x, the expansion ratio of neighbouring cells-

d_1 = x * d_2
d_2 = x * d_3

...

d_1 = x^(n-1) * d_n


Now, the length of a block is the sum of the lengths of the cells.

L = sum[i=1..n] { d_i } = sum[i=1..n] { d_n * e / (x^(i-1)) }

Maybe, my equations are not entirely correct, but this way, you can derive relations between block length L, element number n and cell length at one end of the cell d_n.
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Old   February 14, 2014, 13:05
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Euan Foster
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Ah yeah I thought it was a geometric series or something like. Been a while since I have done them.

I found this post that allows for all that to be done automatically - BlockMesh grading calculator

In some of my sections though I need it to be fine at the start then become more coarse and end fine again. Can this be done without splitting the block up into two separate blocks??

Regards,

Euan.
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Old   February 14, 2014, 13:23
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Gerhard Holzinger
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You could define a cellSet and use refineMesh to refine the cells of the cellSet.
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