Fluid divergence - avoiding race conditions

[danw]

Hi all, wondering if anyone can think of a neat solution to this.

 

I'm attempting to drive the divergence of a smoke sim using various combinations of density and/or temperature... I'm after quite a rapid expansion, but one that starts rapidly and then loses energy.

I something get close using temperature to drive divergence, with a rapid cooling rate for the temperature itself, but the moment I push it too far, it will explode entirely.  Because the divergence will literally create more density/temperature out of nothing when it solves, I end up with a race condition where the faster it expands, the more temperature there is, and it expands even faster next frame.

 

Is there any way to have a rapidly divergent sim, but one where the expansion is normalized, so that the density/temperature channels effectively contain the same total amount, just spread more thinly?  That way I could avoid a feedback look, and just crank the values up until it looked right.

[eetu]

One idea; subtract divergence from temperature, it'd even be a bit physically inspired

[danw]

I'm toying around with dividing the temperature by divergence somehow... but it doesn't seem to be achieving much.  Maybe I should just try a straight subtraction as you suggest... I'd just love to know if there was a mathematically accurate way to do a straight-up preservation-of-mass thing, or better yet, I wish it was just built in to the gas projection microsolvers already, as I tend to just stare in abject horror when attempting to work out mathematical notation myself :-)

 

What would it boil down to I wonder... how much extra volume would a divergence value of 1.0 expand a single voxel to per timestep, or per second...?

 

I just have this feeling that the true answer is going to involve dividing by divergence-values^3 or something.

[danw]

Hmm, well I seem to have managed to build something that seems vaguely self-regulating...

 

Pre-advection, I multiply both the density and temperature channels by a volume derived from:

1/((divergence*timestep)+1)

 

I can then set divergence to whatever large multiple of the temperature at the sourcing stage, and it will have a more and more violent effect, while still rapidly disipating the shockwave, rather than exponentially accelerating it and causing a feedback loop.

 

Very likely would have mathematicians facepalming, but it seems it might do the job for now :-)