I have been going over the theoretical foundations quite a bit this week. Reading papers and generally taking note of what different people do for boundary conditions. I have also done quite a bit of testing with very small particles and large particles.

I found one very big problem. At boundary and free surfaces, the density is "smoothed". This creates big pressure gradients at the surface and can cause big problems for initial conditions. However this is well known in the SPH literature and is called the particle consistency problem.

One method of fixing it is to consider the Taylor series and you get a reasonably simple expression for density. But the equations become implicit, and thus solving systems of equations are required. Instead I use the correction from the previous time step and thus is just a estimate. This works very well for density, but when I use the corresponding expression for the grad operator, I get nothing but instability. The expression can be 0/0 and the correct limit is 0, but numericaly.....

So at this point I only use the correction for the density and I'm getting some very nice results. But I will do some more work on proper correction of partial derivatives and attempt to get that working.

## Thursday, September 15, 2005

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## 2 comments:

Hi there!

After I had a try with N_T's new fluid simulator in Blender I'm quite interested to see how yours perform.

The solution of the solver and the resulting images would be interesting, too.

Work on! The current blender fluid simulator is not perfect.

yea, thanks. I was not really expecting to get anyone on this blog site untill after a release. It will do what N_T's does not, but it will be a bit slower. Also the emphasis is not on "good" looks. There is one nice thing though, it interacts with animated objects and it has its own, simple rigid body dynamics with floating.

The hardest, or rather the slowest and most boring part is the GUI.

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