Navier-Stokes on the Screen
Navier-Stokes on the Screen
(OP)
In a Discovery Channel show looking at movie making their was a segment on the movie Pirates of the Caribbean especially the Maelstrom scenes. I was a little surprised when the Industrial Light and Magic guide stated that all the water scenes were created by using the Navier-Stokes equations, not art. This inclued all the sea states, wave action, boat actions (wakes and bow waves) and especially the Maelstrom Vortex. I just can't comprehend the number iterations required to accomplish this. I know that ILM has one of the largest available computing power around, but wow.





RE: Navier-Stokes on the Screen
There is not a closed-form solution to Navier Stokes. There is not a closed-form solution to very many of the derivative terms within the Equation. For the effects you talk about he was probably using a CFD model that has many important simplyfying assumptions. The model most likely boiled Navier Stokes down to the Euler equation (a precursor to the much more useful Bernoulli equation) by assuming incompressibility and constant friction among other things. The constant friction assumption allows real-world-ish solutions to the interaction between the fluid and an included bouyant mass (i.e., the ship). Bernoulli would not allow that interaction since it has a zero friction assumption.
Pirates did not use Navier-Stokes directly in their fluid modeling even if they think they did, solving Euler that many times is a pretty amazing feat.
David
RE: Navier-Stokes on the Screen
I think even the guys at Stanford wouldn't try to pass off Bernoulli as Navier-Stokes. Don't underestimate the money at stake. At least as much as a medium offshore platform can be made. I'll put my money on Navier-Stokes.
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"Pumping accounts for 20% of the world's energy used by electric motors and 25-50% of the total electrical energy usage in certain industrial facilities."-DOE statistic (Note: Make that 99% for pipeline companies) http://virtualpipeline.spaces.live.com/
RE: Navier-Stokes on the Screen
http://blogs.zdnet.com/emergingtech/?p=824
RE: Navier-Stokes on the Screen
For anyone who is reading this who may not have seen the horrible equation under discussion since college, I've attached a copy of the equation in Cartesian coordinates (which is the simplest representation for this particular problem). There are 7 unknowns, each of which is a function of time, position, temperature, and pressure.
The general form is the ultimate tough nut to crack and the guys at Stanford did not claim to have cracked it. They said
The inviscid form of the equations is Euler's simplification.
Don't get me wrong, what they did was truly amazing and the visualizations were stunning, but they did not and did not claim to have solved the generalized form of Navier-Stokes. The reporter simply grabbed a couple of impressive sounding words and used them inappropriately without qualifications.
David
RE: Navier-Stokes on the Screen
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"Pumping accounts for 20% of the world's energy used by electric motors and 25-50% of the total electrical energy usage in certain industrial facilities."-DOE statistic (Note: Make that 99% for pipeline companies) http://virtualpipeline.spaces.live.com/
RE: Navier-Stokes on the Screen
I love'em when they talk about what they don't know and it seems they mastered the argument.
RE: Navier-Stokes on the Screen
I understand one has to keeping feeding a GeeKal.
http://nyjm.albany.edu/j/2001/7-18p.pdf