Navier Stokes Solved -

Paul Scott

Paul Scott

Senior Member
Joined
Sep 18, 2004
Posts
648
Reaction score
125
Location
San Juan Island, Washington
What happens now in the boat design world? ( unless there’s already a thread going…)
 
A huge number of computational methods suddenly become more reliable. But that doesn't necessarily mean a Great Leap Forward (tm) for Naval Architecture.

Boats operate in real waters, which are never completely homogeneous - density, temperature, salinity and many other physical quantities vary from point to point.

Nor are waters ever completely calm. Statistical methods will still be required. Navier-Stokes is of little help here.

Loads are never static, so NA's will still need to apply their learned knowledge and the experience they have accumulated to design problems.

In short, the solution of the Navier-Stokes equations will, IMO, have an effect varying from miniscule to irrelevant (+ a safety margin) to Naval Architecture and boat design in the large.
 
It would work in a theoretical perfect physical system. However, we work with approximations, so all that is necessary to design a boat is "good enough".
 
Paul Scott said:
What happens now in the boat design world? ( unless there’s already a thread going…)
Click to expand...

Absolutely nothing; because boat design is only minimally connected to hull drag. Hull drag is what is left to evaluate after all the other things that are necessary are stuffed into the too small sock. And, as Leo states, N-S of the water is only a small part of what makes up the total drag; or any other hydrodynamic topic. The fact that you are 1% more sure of 5% of the problem is not an earth shattering revelation.
 
Last edited:
Leo Lazauskas said:
But that doesn't necessarily mean a Great Leap Forward (tm) for Naval Architecture.
Click to expand...

God I hope not. I really don't think there are 15 million to 55 million Naval Architects out there to starve to death.

Great Leap Forward - Wikipedia

en.wikipedia.org en.wikipedia.org

Edit 20260909; defined how they would die...seeing it's the 50th anniversary of Mao Zedong's death.
 
Last edited:
Okay, a piece of the N-S millennium problem was tackled (an 80 year-old open problem), but the result is not what we were hoping for - the smoothness conjecture appears to be false. Singularities can manifest in a viscous field in finite time with only smooth forces applied. A related problem pertaining to non-viscous fluids and no forces was also cracked and also disproved. The basic issue is that conditions become so extreme so quickly that the continuum model of fluids no longer applies. The Navier-Stokes model doesn't break physics, it just drives it into the realm of statistical mechanics. The model's assumptions about the fluid environment are no longer consistent with the environment that the model produced.

The physicist in me guesses that there will have to be checks and error handling added to a lot of code. The engineer just wants to know what can we do with this new feature? When will we get a new singularity operator to play with?

Can we actually exploit this - like build a cheap medical particle beam that's worth a damn or produce containable fusion plasma?

Oh, we still don't have an existence proof yet, do we? We don't actually know that all input scenarios actually produce a unique output.
 
Last edited:
The singularity they found seems to be at the center of a vortex (a well-known spot for singularities in inviscid flows)

https://openai.com/index/navier-stokes-solution/

How do we know that the problem is with the equations themselves, not just with their attempts at numerical solutions?
 
Doug Halsey said:
The singularity they found seems to be at the center of a vortex (a well-known spot for singularities in inviscid flows)

https://openai.com/index/navier-stokes-solution/

How do we know that the problem is with the equations themselves, not just with their attempts at numerical solutions?
Click to expand...

Correct; which leads to the adoption of vortex solution methods by NASA (and other organizations) for high Reynolds number fully submerged bodies where the TBL is "small". But just exactly where and when that transition takes place for "useful" size and speed of objects is subject to much debate. And, given the totally chaotic nature of fluids in the real world, perhaps realistically unknowable but boundable. I wonder how a LLM like that used on the N-S solution would handle the Admiralty Coefficient.
 
Navier-Stokes considers the fluid as continuum. In reality, it is made of relatively large molecules. Any solution will be an approximation to the real system. Pressure and friction are statistical values. It breaks down below a certain size.
 
gonzo said:
Navier-Stokes considers the fluid as continuum. In reality, it is made of relatively large molecules. Any solution will be an approximation to the real system. Pressure and friction are statistical values. It breaks down below a certain size.
Click to expand...

That is why I have always liked the "magnetic marble" model of water in hydrodynamic calculations.
 
jehardiman said:
That is why I have always liked the "magnetic marble" model of water in hydrodynamic calculations.
Click to expand...
How accurate are the predictions with that model?
 
Doug Halsey said:
Please tell us you're joking!
Click to expand...
No, I'm not. A model should always be selected based on what info you are trying to get out of the model. N-S if fine for smooth, continuous fluids but unsuitable for things like breaking wave splash or cavitation.
en.wikipedia.org

Smoothed-particle hydrodynamics - Wikipedia

en.wikipedia.org en.wikipedia.org
en.wikipedia.org

Volume of fluid method - Wikipedia

en.wikipedia.org en.wikipedia.org
gonzo said:
How accurate are the predictions with that model?
Click to expand...
Accurate enough to make engineering decisions. As a Naval Architect designing ships, we only need to limit bound the problem... we don't need the exact answer at that exact instant in time. This is the whole reason why 0.15 m is the minimum initial GM under the general criteria of Part A of the 2008 International Code on Intact Stability for cargo ships and other class/IMO rules...they cover a statistically large portion of the possible engineering issues. I became convinced of that many years ago when I was involved in a on again/ off again running friendly feud with a PhD hydrodynamicist. I admitted that my solution was crude, inelegant, and not correct and he admitted that my solution, though incorrect, bounded the statistical upper limit of a random process.... which had to be designed for anyway.

(EDITED for typos, no content changed.)
 
Last edited:
As an engineer I understand your position. We work with statistical values. Most of the time the values are specified by the manufacturer, and we accept them for the design calculations. For example, steel beams are not individually tested. At most, there may be a small percentage checked for compliance on a critical application.
 
You must log in or register to reply here.
Forum posts represent the experience, opinion, and view of individual users. Boat Design Net does not necessarily endorse nor share the view of each individual post.
When making any potentially dangerous or financial decision, always employ and consult appropriate professionals. Your circumstances or experience may be different.

    • Back
    Top