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 dancfd July 9, 2012 23:09

BlockMesh Grading Ambiguity: How to Get Desired y1

Hello all,

I am having trouble getting blockMesh to produce the right y1 for my mesh. If I follow the equations in the User Guide 2.0.0 section 2.1.6.2:

Desired y1: 0.0006996
Desired cell size of last cell: 0.15
l = 1.499364 % Length of block
n = 100 % Number of cells

Therefore:
R = 0.15 / 0.0006996 = 214.408 % ratio of last to first cell size
r = R^(1/(n-1)) = 1.0557179202 % ratio of each cell to its neighbour
Alpha = R (R > 1)
Delta_x_s = 0.000370711 % Size of smallest cell

Here is the issue: Delta_x_s is supposed to equal my desired y1. The problem is blockMesh grading uses a ratio, R, to define the grading. Therefore if the same factor is applied to both first and last cell, blockMesh will not know the difference: R is the same. The only way to adjust the y1 is then to change the number of cells, I suppose - but that leaves me no control over the number of cells. Is there any way to control both the number of cells and y1?

Thanks,
Dan

 rob3rt 0ng December 31, 2012 04:26

Hi Dan,

Have you figured this out, if you have then please share ;)

Happy new year!

Robert

 dancfd January 2, 2013 21:41

Hello Robert,

Happy New Year,
Dan

 kalle January 4, 2013 02:45

Quote:
 Originally Posted by dancfd (Post 370549) ... Is there any way to control both the number of cells and y1? ...
Stupid answer is; adjust the length of the edge. More useful answer may be: divide the block in two, where the block close to the wall has grading such that you get delta_x_small and delta_x_large as you like, and the outer block has no grading and all cells with size delta_x_large. (or optionally also a grading, which is different from the wall block)

K

 rob3rt 0ng January 5, 2013 04:53

Hi Karl,

But that would increase the aspect ratio both and eventually will affect the convergence, wouldn't it? Isn't there anyway to control y+ without increasing number of cells and without getting a high enough aspect ratios? Sorry for the rather impetuous question.

Regards,
Robert

 kalle January 5, 2013 14:49

You mean that the cells next to the wall becomes kind of pancake cells? That is a de facto standard of achieving near wall resolution in more or less all types of meshes. This is generally also ok, as derivatives are largest in the wall-normal direction.

If you want isotropic cells to the wall (like in the case of wall-resolved LES), you can use refineHexMesh on cells adjacent to the wall. Then you will get polyhedral cells in the interface between refined and non-refined cells (hence breaking the constraints of pure hexahedral mesh). Of course this may lead to vast amount of cells.

K

 linuxpirates June 4, 2014 01:04

I appear to be slightly late to the party, but it's very simple.

If you have a length L, and divide it by N elements, each element will have a size L/N.

Applying an expansion R across the entire length L, means that the first element will have a size (L/N)/sqrt(R) and the last element will have a size (L/N)*sqrt(R).

As proof, consider the ratio of the sizes of the first and last elements, you have:

(L/N)*sqrt(R) / (L/N)/sqrt(R) = R

Hence, if you want to prescribe your desired y1, you would do:

y1 = (L/N)/sqrt(R) -----> R = L^2 / (N y1)^2

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