BlockMesh Grading Ambiguity: How to Get Desired y1
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 188.8.131.52:
Desired y1: 0.0006996
Desired cell size of last cell: 0.15
l = 1.499364 % Length of block
n = 100 % Number of cells
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?
Have you figured this out, if you have then please share ;)
Happy new year!
Unfortunately I have not found a solution.
Happy New Year,
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.
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.
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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