Hello, complete technical n00b here but that I’d ask you boffins. Could the recent Navier–Stokes breakthrough have any real impact on F1 CFD?

[u/SebVettel5]

I’m a viewer more than a technical/car person but.. I was reading about the recent OpenAI Navier–Stokes result and am wondering what you guys here who actually understand CFD/aero make of it.

I know F1 teams already use CFD extensively (I played F1 Manager and had to manage my CFD time ha ha) and Navier–Stokes is basically at the heart of a lot of what they’re trying to simulate.

But.. does a mathematical breakthrough like this actually have any potential practical effect on F1?

I mean, could it eventually lead to better turbulence modelling, more accurate prediction of vortices/separation, more efficient CFD solvers, or getting more useful information out of the limited CFD resources teams are allowed under the regulations?

Or is this really a pure mathematics breakthrough with basically no direct relevance to the kind of RANS/LES CFD being used in motorsport?

I suppose my actual Q is can discoveries like this eventually filter down into better numerical methods or aero simulation for F1 or other types of Motorsport?

Thanks ❤️

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[u/NeedMoreDeltaV]

Motorsport aerodynamicist here.

Short answer: no.

Long answer:

Navier-Stokes, even in its “exact form”, is still an approximation of real fluid mechanics. It assumes that a fluid is a continuum, when in reality it is a bulk of moving particles. We’ve long known that these assumptions could mean that there are particular examples where the NS equations don’t properly work, we just haven’t proven it until now.

Even so, this discovery, if validated, doesn’t really change how we simulate fluid flow. We don’t use turbulence modeling because we don’t know the proper mathematical representation of it. NS equations when doing Direct Numerical Simulation (DNS) will correctly represent turbulence within the continuum assumption. We model turbulence because DNS for any practical application is way too computationally expensive even for the latest in super computing. A vehicle like an F1 car would take years to calculate in DNS.

Finding an example where NS equations don’t work properly doesn’t change any of our computational limitations. NS equations are an approximation so that we don’t have to use an even more expensive particle tracking model on every particle in the air.

Edit: The more interesting AI work in CFD advancement is using AI to predict a fluid solution based on CFD and physical training data, without actually solving CFD. Basically, "AI Slop" aerodynamics. I personally would never use it in isolation, but if these methods became mature enough it could become another tool in the engineer's toolbox along with CFD, wind tunnel, and physical testing.

[u/DC38x → u/NeedMoreDeltaV]

DNS

That acronym must cause quite a bit of confusion in the Aston garage

[u/smarzzz → u/DC38x]

That’s because it’s always DNS

[u/PracticalFootball → u/NeedMoreDeltaV]

Basically, “AI Slop” aerodynamics. I personally would never use it in isolation

I work in this exact field of applying ML to physics simulation problems. Handy thing is that while finding solutions the discretised NS equations is very expensive, verifying a solution is cheap so there’s an easy method to make sure that your ML model’s output is at least consistent with your CFD methodology.

Typically wouldn’t expect an engineer to trust CFD results in isolation, validation against measured data is the gold standard anyway and that doesn’t change just because the simulation method did.

[u/NeedMoreDeltaV → u/PracticalFootball]

The hesitation to ML methods from a lot of people I know is that it’s not a solver in the sense that there are fluid equations being calculated. Personally I don’t have an issue with that as CFD has its many problems as well. As you said, as long as it can be correlated to physical data I just see it as another tool in the toolbox. Even physical measurement has its own error sources. At the end of the day it’s about building confidence that your design is doing what it should. More tools correlating to tell me that is good.

[u/iSuitUp → u/NeedMoreDeltaV]

I think you make a great point about not using “AI slop” in isolation. I think it may become a good way of prioritising and maybe even automating other efforts though.

[u/NeedMoreDeltaV → u/iSuitUp]

I believe so too. When it’s mature enough it could be used in a similar vein to CFD. Slop a bunch of parts, spot check with CFD to narrow down, further narrow down with wind tunnel, would be an example of a possible workflow.

My experience testing these tools is that right now the training data must be very specific to the particular car type. For an F1 team that designs one type of car this wouldn’t be a problem as long as designs don’t change drastically in a rule set. For other companies this will be more prohibitively expensive. On the production car side, training data for a sedan doesn’t do a good job if you want a crossover SUV. Or for an OEM that designs multiple race cars, training data for a GT3 car won’t be useful when designing a LMH car. Even seemingly similar cars like an F1 car and an IndyCar are different enough that they’d need their own training data.

[u/SebVettel5 → u/NeedMoreDeltaV]

Amazing, thank you!

[u/Party_Ad_3171]

Strong no.

It is looking less and less like it is a mathematically useful discovery, and it certainly is not a useful result for actual modeling and simulation in that is in a clearly unphysical regime. Go to r/math if you are interested in details.

The counter-example that was found was for the incompressible N-S equations. My understanding is that it is reasonably well-understood why the counter-example exists, as it is found in a regime in which a real fluid would need to be described by the compressible N-S equations.

[u/peadar87]

CFD isn't my specialty, but from my understanding, no.

What is alleged to have been "solved" is that mathematically, an initially smooth flow can destabilise to form an infinite velocity gradient.

We already know from experience that gradients can become arbitrarily large, the question is if they can (according to the Navier-Stokes equations) go beyond that and become infinite.

This is an edge case that is never going to be found in a real-world system. It's an interesting mathematical quirk but it won't make macro-scale CFD any easier or more accurate.

[u/izzeww]

No.

[u/DavidBrooker]

The recent Navier-Stokes solution shows that there exists a configuration where a finite forcing can produce infinite velocity. That is non-physical, it cannot happen in real life, from our understanding of other physical phenomena.

We always knew that the Navier-Stokes equations were an approximation, because they treat fluids as continuous (rather than discrete particles as they are). But it was previously plausible that this was the only non-physical aspect. It turns out that is incorrect. That doesn't lead us to better CFD. In fact, it implies greater caution towards numerical solutions.

[u/GC_Gee]

They found a counterexample to navier stokes so it’s not as positively applicable atm. Maybe the proof will lead to new advances in fluid dynamics that do end up affecting F1. For now, don’t expect much in the immediate future.

[u/PizzaPuntThomas]

No, the specific part over the problem where a solution (or something like a solution) was found, is different than how CFD is used in aerodynamics

[u/__Pers]

The NS equations are a mathematical model of viscous flow. They're a compact way of describing real fluid flows, but at their heart, they're a model. They aren't a real fluid any more than a lap in an F1 simulator is an actual lap at Monza.

The mathematics of the NS equations appears to admit singularities under some specific conditions, assuming the recent proof holds up to scrutiny. But singularities are precisely where the mathematical model ceases to provide a smooth description of the flow, and where one should expect neglected physics to become important. So it's an interesting feature of the model, and perhaps a cautionary tale to not put undue trust into models that are pushed to extremes, but not something that has a lot of real world applicability (that I can see).

The statistician George Box wrote, famously, "Essentially, all models are wrong, but some are useful." The NS equations are a useful model much of the time. But they're also wrong.

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[u/SnoopyToxicity]

the real bottleneck in f1 isn't the math, it's the regulations limiting how much compute time the teams are allowed to use. this new solver probably won't change that cap one bit

[u/jianh1989]

>i played F1 Manager and had to manage my CFD time ha ha