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#1 |
Member
ishan
Join Date: Oct 2017
Posts: 77
Rep Power: 8 ![]() |
I am trying to understand the equations behind the total expansion ratio calculation and simpleGrading in general. I know that the grading is based on geometric progression.
The following quantities are of interest to us: ![]() ![]() ![]() ![]() ![]() ![]() The common ratio is: ![]() In the above equation, ![]() The summation of all the geometric terms( cell lengths in this case) is the length of the edge ![]() ![]() If we know ![]() ![]() ![]() ![]() ![]() We can numerically find the root of the above polynomial which will give us the value of ![]() ![]() ![]() Now the issue is that when I tried to solve the above polynomial equation numerically(Newton's method), it finds the root but it's values does not match with the grading calculator script here https://openfoamwiki.net/index.php/S...ng_calculation.I tried to dig deeper into the code of the calculator but I understood very little. The reason why I want to know more about this is because I want to automate a portion of my grading using a Python script since I have a lot of blocks to generate the grading for. Can someone please point me in the right direction ? |
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#2 |
Senior Member
Hrvoje Jasak
Join Date: Mar 2009
Location: London, England
Posts: 1,906
Rep Power: 33 ![]() |
Sure. My old friend Cedo says the most human way to define the grading is the size ration of the first to last cell. This, grading ratio of 5 means that the last cell is 5 times larger than the first. For the opposite effect, you would use 0.2
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Hrvoje Jasak Providing commercial FOAM/OpenFOAM and CFD Consulting: http://wikki.co.uk |
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#3 |
Member
ishan
Join Date: Oct 2017
Posts: 77
Rep Power: 8 ![]() |
I just checked the user guide and this explanation matches with the definition of the total expansion ratio. Thank you !
How would we approach the problem if we have the first cell height , the edge length and the number of cells? Mathematically, I don't see any other way other than solving for the root which, would be the common ratio. |
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#4 |
New Member
Join Date: Jan 2024
Posts: 1
Rep Power: 0 ![]() |
The grading calculation formulae employed by educational institutions can differ depending on the grading system and the specific criteria applied.
https://www.calculatorcube.com/ |
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Tags |
blockmesh simplegrading |
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