[Peacekeeper]

Hi!
This is my first post in this forum, so I really appreciate any help. This problem is driving me crazy in the last days. And sorry for my English …
As a hobby i´m trying to improve my python (3.3) skills and my knowledge in fluid dynamics. Recently I discovered some interesting paper concerning SPH (Smoothed Particle Hydrodynamics).

http://software.intel.com/en-us/arti...-games-part-15
http://obswww.unige.ch/lastro/confer...f/lecture4.pdf

The Internet is full of it, so I decided to create my own very basic version of it. My goals are:

- Acceleration only based on the pressure gradient for now (tough enough! )
- Collision, viscosity and not using euler integration is scheduled for later…
- Thanks to numpy a fast nearest neighbor algorithm is already integrated

But after getting the first (rather unstable) results I begin to wonder if I really understand the math behind it. I will begin with the two most basic things to do in sph - get the density and pressure with the kernel.
Regarding the density I used this equatation:

With a spiky kernel (q = r/h for normalization)

After blindly programming everything the results worry me:

How can I compute density by rather random weighted functions? How can I compute density by adding weighted point masses together? In the end I still have a mass. If I increase the range h I get information from more and more particles so the “density”-value will rise. Some kernels return “1” for zero “q” (= maximum value of W) some return random values like “3.92”. So I get totally random values for my particle density. In my head as an (unprofessional) example it looks like this:

Shouldn’t I somehow tie the accumulated masses to the observed volume (or surface) to get the density? But I have not seen that in the codes I looked at:

"dist = particle.Position - ((FluidParticle) particles[nIdx]).Position;
particle.Density += particle.Mass * this.SKGeneral.Calculate(ref dist);”

Most authors use this to calculate the pressure afterwards:

P_0 ist called the rest density and usually 998 kg/m³ for water. Then it really stops making any sense to me:

Pi=k * (0.0217 kg(?) -998 kg/m³ ) .. äh what?

Result is obviously a totally wrong pressure.
My next question is how to use a gradient when I have no scalar-field but a simple function W(r,h). I think I did it the right way but before I go into that in detail I hope my most noobish questions can be answered

Greetings
JP