Navier-Stokes on the Screen

[unclesyd]

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.

 

[zdas04]

Just because children use words that they don't understand really doesn't imply that they understand the concepts.

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

 

[BigInch]

In the end, it took a team-up of Industrial Light & Magic and a squad of computational physicists from Stanford University to teach computers to generate mathematically perfect water, based on a powerful set of rules known as the Navier-Stokes equations. Performing the simulation required thousands of computers running simultaneously - doing a job that would have taken a single computer about 1,000 years. The actual ships were then layered on top of those images. The result: a believable depiction of something that could never happen in the real world.

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.

**********************
"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/

 

[unclesyd]

Toward the bottom of this article is a link to a paper with the method use by the team for the water effects.

http://blogs.zdnet.com/emergingtech/?p=824

 

[zdas04]

I'm enough of a fluids geek to have enjoyed the paper, thanks syd.

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

Our fluid solver is predicated on previous grid-based Navier-Stokes implementations such as [40], which ignore viscous effects and use the inviscid form of the Navier-Stokes equations

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

 

[BigInch]

Ya. Reporters are experts at that.

**********************
"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/

 

[Giuliano81]

We could call the reporter to help us solving our problems in fluid mechanic!

I love'em when they talk about what they don't know and it seems they mastered the argument.

 

[unclesyd]

zdas04,

I understand one has to keeping feeding a GeeKal.

http://nyjm.albany.edu/j/2001/7-18p.pdf