# Can similarity criterion help reducing calculations in Finite Element Analysis (FEA) problems?

Can similarity criterion help reducing calculations in Finite Element Analysis (FEA) problems?

I'm using NX (a thermal and CFD simulation software) to simulate the temperature and fluid field of a LED application.

It takes a long time each time i change something. I'm wondering if I can reduce the calculations by scaling down the object I'm calculating.

For example, if cooling solution A is best for an application of size 10. Is the cooling solution A also the best if I scale down the application to size 5?

If this is true, then i can base my calculations on size 5 and reduce drastically the time of calculation.

I believe this is not so simple. For example heat pipes behave differently with different lengths.

But maybe with some corrective parameters, this can be done. Any advices ?

(I realize that this might not be the place to ask this question, please also advice where i can post this question)

• A first guess is that a similarity criterion or rescaling cannot be used to speed up the calculations. The speed is determined by the number of subdivisions, convergence and precision you want to achieve. So your size 5 or 10 does not influence either of those. At the same time you can expect different physical behavior for different dimensions, e.g. the Reynolds number might change and the properties of fluid flow depend on the physical size of your pipes, etc. Jul 3 '12 at 9:07
• Thank you for the answer. I don't quite understand your first comment. Say for example the size of the step is 1.2mm, then there's definitly less calculations for a box of size 5cm and a box of size 10cm. As for the second comment, yes the physical behavior will change. But i think to some extend, one optimal design will remain optimal for other dimensions. By "optimal design", i mean for example a "V" shaped sink instead of a upside down "V". The size will change but the principal will not, here i mean "V" is always better than an up side down "V".
– osager
Jul 3 '12 at 9:11
• and my problem is to select the optimal design with the highest cooling efficiency among several possible shapes. but since the original shape is quite large, and the calculation takes several hours. I want to reduce the size and compare. I wont reduce too much, only like half of the original size.
– osager
Jul 3 '12 at 9:24
• Hi Alexander, that's what i mean. With the same step size, 5cm will have less subdivisions. Is there an easy way to repost this question on scicomp ?
– osager
Jul 3 '12 at 9:54