# Eq 27 of the User Guide seems incorrect

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June 9, 2008, 03:51
Description: I think Eq. (2.
#1
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Takuya OSHIMA
Join Date: Mar 2009
Location: Niigata City, Japan
Posts: 518
Blog Entries: 1
Rep Power: 11
Description:
I think Eq. (2.7) of the User Guide (page U-39), one of a set of equations to find the size of the smallest cell for a graded mesh,
alpha = R<sup>n</sup> (for R > 1), R<sup>1/n</sup> (for R < 1)
should be written as
alpha = R (for R > 1), 1 - r<sup>-n</sup> + r<sup>-1</sup> (for R < 1)
(note the case difference for R and r).

Solver/Application:
blockMesh

Source file:
None

Testcase:
The calculated size of the smallest cell using Eq. (2.7) according to the cavityGrade settings written in the manual i. e.
Quote:
 For the cavityGrade case the number of cells in each direction in a block is 10, the ratio between largest and smallest cells is 2 and the block height and width is 0.05 m. Therefore the smallest cell length is 3.45 mm.
is in fact 3.62 x 10<sup>-6</sup> m, which obviously is different from 3.45 mm. On the other hand with the corrected equation the calculated size agrees with the value. The corrected equation can be easily derived using the formulae for geometric series.

Platform:
all

Version:
OF 1.4.1

Notes:
I hope I'm not making silly oversight, misunderstanding or mistake (quite likely!) since the error looks too trivial...

Takuya

 June 9, 2008, 11:29 I got the same thing and was g #2 Senior Member     Marco A. Turcios Join Date: Mar 2009 Location: Vancouver, BC, Canada Posts: 727 Rep Power: 18 I got the same thing and was going to post on the board, but forgot about it.

 June 9, 2008, 13:32 Dear Takuya, The User Guide #3 OpenFOAM discussion board administrator Guest   Posts: n/a Dear Takuya, The User Guide will be updated in the next version. Thanks for bringing this to our attention.

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