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# SPH paper...notation issues.

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### #1cluelessWanderer  Members   -  Reputation: 111

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Posted 24 May 2012 - 08:01 PM

So i was reading an sph paper(link: http://www.matthiasm...tions/sca03.pdf) and everything was going well untill i reached the equations for the smoothing kernel.

--The image of the equation is an attachment. Appearently i can't link images from imageShack.--

I've never seen piecewise functions like this before.
So bolded "r" is supposedly a displacement vector and "h" is the support radius( a scalar).
This begs the question,what is the unbolded r in this equation? The distance?

So assuming r is the distance between two particles...
If r is between 0 and the support radius "h" i compute (h^2 - r^2)^3 and then multiply that value by (315 / 64*pi*h^9) ?

Also the paper doesnt give the gradients for the smoothing kernels so i guess i have to take them myself(assuming the del operator is the gradient in this paper)?

after looking back at the article im confused to what the del operator actually does.
If you refer to eqn (15) the right hand side of that equation evaluates to a scalar. right?
If thats true then how does a scalar become a vector after the del operator is used(eqn 16)?

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Edited by cluelessWanderer, 24 May 2012 - 08:23 PM.

### #2luca-deltodesco  Members   -  Reputation: 624

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Posted 25 May 2012 - 05:51 AM

Your interpretatino of (20) is correct.

Del operator is the gradient, and (15) computes a scalar yes, but the del of that equation is a vector:

If you have a function F : R^3 -> R
then del F : R^3 -> R^3, del F = [ p/px F, p/py F, p/pz F ] as the vector of partial derivatives of F.

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