12-06-07, 07:29 PM
Here is a paper:
The Numerical Simulation of Turbulence
It has a bit about filament formation through gravitational collapse. Some of the grid sizes are sweet... 2048^3!
I wonder what a solid ball would do to this type of turbulance at supersonic relative velocity.
12-06-07, 08:40 PM
I scanned the article---the pictures are pretty interesting.
I wonder---the pictures obviously look like smoke. I suppose there's a parallel he's trying to draw between structure formation (i.e. filaments we see in SDSS, for example) and fluid dynamics?
12-07-07, 10:50 AM
I would think so. I think that a major conclusion is that as gravitation overcomes pressure, turbulence increases greatly. I think maybe his point is that turbulence is generally overlooked, and should be included in further cosmic simulation. I know that's not very technical, but the author would be a much better source of information / opinion.
So filaments are explained by turbulence?
12-07-07, 12:15 PM
Rather, assuming you're not being sarcastic:
"Non-linear turbulent interactions stretch and fold the large-scale eddies produced by stirring into thin vortex filaments"
Stirring produces eddies, turbulence produces folding of eddies, folds produce/are filaments.
I suppose the answer would be "yes".
I think what he's getting at is that LES is a great vorticity approximation method, but that it does not cut it for cosmic simulation.
I would ask the author for his opinion on the matter though.
That's cool. I am no expert and have no idea what I am talking about, but "gravitational fluid" should behave different than normal fluid right?
12-08-07, 10:33 AM
Not particularily no. The Navier-Stokes equations that are normally used for fluid simulation have a term on the right hand side for miscellaneous body forces including gravitation (usually labelled f or g). Super useful introductions to this field are contained in GPU Gems 1 2 and 3. Jos Stam also has a paper called "Real-Time Fluid Dynamics for Games". All of these come with some form of source code, which I found to be more useful in helping me to learn than any of the pure math notation or English.
The critical part of this simulation was the way they modeled turbulence. A lot of other simulations will use large eddies (Large Eddy Simulation) of relatively small complexity to act in substitute for the countless little eddies that do exist in real turbulent flow. Because large portions of turbulent space are simplified as such, local non-linear turbulence effects are removed (it's the non-linear part that's hard to solve, but definitely the most interesting). In this simulation, non-linear turbulence effects are allowed to run rampant, which resulted in interesting structures.
I'm not sure exactly how different this simulation is from previous work, but if it does have something new to say about modeling turbulence without simplification, then the Clay Institute's Millenium Prize related to this field might be claimed.
...Because large portions of turbulent space are simplified as such, local non-linear turbulence effects are removed (it's the non-linear part that's hard to solve, but definitely the most interesting)....
The numerical solution of fluid turbulence isn't big problem for current computers, it can be done (with some optimizations) even as a Java applet (http://superstruny.aspweb.cz/images/fyzika/simulace/liquid.htm) at the web page and the solver algorithm is rather simple. The strictly causual (i.e. consecutive) math isn't proper tool for modelling of large parallel systems composed of many particles, like the fluid turbulence of Aether phase transforms.
12-08-07, 03:58 PM
Is that simulation pressureless?
The reason I ask is because that application appears to allow for stimulated advection (like in the GPU Gems example), but not actual rarefactions / pressure differences. Perhaps my idea of turbulence is not quite correct. I thought turbulence required divergence (in the linear algebra sense), like when an airplane drops suddenly due to a decrease in the surrounding air pressure.
What I meant was that in normal fluid the particles interact via a complicated electromagnetic forces, while in gravitational fluid particles interact via only gravitation. These two interactions are very different.
12-09-07, 01:39 PM
I think that's a fair conclusion.