What makes the Navier Stokes equation so difficult?

[BWV]

Solving chess is physically impossible but a problem that today takes a year for a supercomputer to calculate will likely be manageable in 10-20 years

 

[Zel'dovich]

... it would take a modern supercomputer years and years to finish the problem. The computation time scales with the cube of Reynolds number.

Sure, maybe Moore's law will someday catch up, but we aren't there yet.

The problem is even worse for more complex technical situations. For example, a DNS of the NS equations for a two-phase system coupled with chemical reactions (which is the situation taking place in a diesel engine or a liquid fuel rocket) could require millions of years with the best currently available super computer. It is a nightmare!

So, yes, maybe Moore's law will someday catch up and we just have to sit and wait for that day. But the question is if this could happen in the foreseeable future. If the answer is no, then you need a plan B.

 

[boneh3ad]

The problem is even worse for more complex technical situations. For example, a DNS of the NS equations for a two-phase system coupled with chemical reactions (which is the situation taking place in a diesel engine or a liquid fuel rocket) could require millions of years with the best currently available super computer. It is a nightmare!

So, yes, maybe Moore's law will someday catch up and we just have to sit and wait for that day. But the question is if this could happen in the foreseeable future. If the answer is no, then you need a plan B.

With a username like that, I'm not surprised you'd pick such an example. Also, it's a good example. It's a problem at very high speeds/temperatures as well, when gases ionize and are multiphase, multispecies, and chemically reacting. Radiation can also become the dominant heat transfer medium.

 

[BWV]

As ‘universal approximators’ are neural networks useful for NS?

https://en.m.wikipedia.org/wiki/Universal_approximation_theorem

 

[Tom Kunich]

In my book, "fine enough as makes no difference" equivalent to "small enough." If it's fine enough to make no difference whether you go finer, why do you think it should go finer?

Well, that's pretty much what I was saying. But you really aren't solving the equation if you don't go finer because you think you can use statistical averaging to make your solution "good enough" don't you think? But of course I'm approaching these problems like the EE I am. I did projects for the military and NASA that were never "good enough" unless they were perfect. When other people's lives are on the line I could never take less than perfect. If I had to run every possible test a thousand times that's what I did. Calculating the drag because of turbulence on a race car only puts you behind someone else with better aerodynamics but not detecting so much as a molecule of poison gas is another matter altogether.

 

[boneh3ad]

I assure you that myself and everyone I know who works with or for NASA, the military, Boeing, Lockheed, Northrop, Raytheon, Ford, GM, Ferrari, Mercedes, and any other organization dealing very heavily with fluids treats the continuum assumption as being "perfect" except in rare circumstances. We will all continue not worrying about individual molecules and using that continuum assumption to design your planes, rockets, missiles, and cars like we always have. Your can worry about individual molecules if you wish.