Monday, February 18, 2008

Smoking, fluid simulations, and other things bad for your health

Readings for Tuesday, Feb 19-

R. Fedkiw, J. Stam, and H. Jensen. (2001). Visual simulation of smoke. Proc. ACM SIGGRAPH, pages 15–22. Related movie. Another.

Chapters 5-6 of Robert Bridson and Matthias Müller-Fischer.


Unknown said...

As with most of the papers on fluids, there is a considerable lean towards "we'll patch the problem" thinking. By this I mean they want to fix the numerical dissipation after it's gone rather than before it happens. Why is this such a hard problem? Is it discretization (or pseudo-discretization) or numerical approximation (the semi-Lagrangian) that causes these dissipation to occur?

For their cubic interpolation they obviously fixed the overshooting problem. However, they also eliminated some of the curvature as a result (look at the right hand sides of the curves especially). Since they are merely clipping, why not keep the normal interpolation and when it overshoots cut it to zero? It seems this would give the same "no negatives" behavior while still preserving all the curvature.

Fluid Course 5&6:
The first thing I noticed is that they answered my above question about numerical dissipation. Another sidenote: their "add 10^-20 to the denominator" solution to divide by 0 is awesome.

Chapter 5 seems to overlap most of the last paper.

Chapter 6 has a notable remark in that it uses geometric methods instead of a semi-Lagrangian (6.2.2). I've been wondering why PDE seems to be so common. These authors claim that geometric methods are accurate and fast, so what is the benefit of using a (semi-)Lagrangian?

Ryan said...

Fluid course 5 -
The extension of fluid methods to smoke given here seemed pretty obvious and straight forward. I was intrigued by the quick side note they mentioned that you can model heat transfer from hot objects and wonder how that would look in the simulation. I'm curious how much hotter your objects would need to be to see the waves of heat ripple through the smoke. The vortex confinement seems like a good idea to reinforce the visual behavior that is not being well reproduced with the simulation

fluids course 6-
For some reason i like the idea of a level set with signed distance better for fluid representation better than particles. I feel like the particles will always be too "big" and miss important small scale details. This chapter mentions that the interpolation in advection will wipe out these same details, and basically for the same reason, but at least I feel like its more hidden in the math, instead of staring me in the face. I do wonder how efficient the calculation of the signed distance can be done, especially if we have to perform it every time step or so.