[JorgeGT]

It is difficult, but there are modeling approaches that work, such as VoF (https://en.wikipedia.org/wiki/Volume_of_fluid_method). Basically, in addition to velocity, pressure, temperature, etc., you store an additional scalar in each cell of your computational mesh representing the liquid's volume fraction. Then, you solve an additional equation to transport that scalar.

[s1291]

Solving the Navier-Stokes equations numerically in 3D is very time-consuming, even on HPC clusters, not to mention the additional modeling required for multiphase flows. Your answer implies that the solutions are obtained almost instantaneously, which is not the case.

[krisoft]

I think the reason these kind of simulations are fast enough is because they are very coarse and approximate. Don't think of asking how exactly the foam swirls around the individual longerons, more like a very rough estimation of which side of the tank the liquid is slumped to. Remember it doesn't have to be "exact" just close enough to be useful.

By their very nature model predictive controllers operate in a world where not everything is perfectly modelled. Engineers do their best and whatever is left is the "error" the controller is trying to deal with.

[JorgeGT]

Oh no, apologies if that was the impression I gave!! I actually perform CFD simulations in HPC clusters, and in fact I'm an admin of the small cluster at my research institute =)

These are indeed heavy computations. What I meant is that VoF is one additional equation to be solved besides the N-S equations (either filtered as in LES or Reynolds-averaged as in RANS), the energy equation, your turbulence model equations, and so on. Certainly, not instantaneous at all, but simply an additional "simple" model that we can hook into our current way of doing CFD.

So, my point was, sloshing is a problem that we know how to simulate, although certainly you need HPC resources. Though, looking at those 100k NVIDIA H100 Elon has, I guess they have them! :P

[jjk166]

They don't need to solve the Navier-Stokes equations, they don't care how the fluid is actually behaving, they just need to approximate how the mass is moving within a margin of error that the control system can handle.

[KeplerBoy]

Maybe the tank is just not a large hollow structure but contains fins/compartments/whatever to restrict the sloshing motion and it's not that big a contribution to the overall motion.

If it's no stronger than a sudden wind gust, it's just something the controller has to be able to take care of without a heads-up.

[nothercastle]

They probably pre solved a bunch of scenarios and interpolate between them known solutions

[WalterBright]

If the computation is too difficult, another approach is build a test stand and try methods until it works.

Which is why we use wind tunnels, for example.

[swader999]

Wouldn't it burn most of the fuel to mitigate the effect?