In CG fluid simulations, one either use grid-based Eulerian methods (Bridson’s book uses a thing called a MAC grid), or use particled-based Lagrangian methods such as SPH (smoothed particle hydrodynamics). They all use the Navier-Stokes equations and the incompressibility condition; the difference is how you approximate it (with tradeoff between realism/performance). Each method has its own quirks (such as the PIC method suffering from unwanted viscosity, and FLIP suffering from numerical instability.) Nowadays the grid-based people use APIC a lot, because it seems to solve both the disadvantages of the two (you can see the links in the comment above)
There's a new trend of using deeplearning to replace and mix the solvers. Some ongoing research looks at tackling the compressible flows. Accelerating lattice boltzman methods with DL is also under study at various labs. See https://github.com/jolibrain/fluidnet_cxx for a reimplementation of fluidnet with aten/Pytorch tensors.
The literature on DL + cfd is growing steadily with some interesting papers at machine learning conferences. We are seeing the first set of applications in industry as well, very exciting !
Fluid dynamicist here. I wasn't aware of the machine learning work you've mentioned. They're addressing an important problem, but I'm disappointed in the paper based on a brief look. I see no comparison against experimental data (validation). Indeed, the cases the authors compute most likely have no corresponding experiments, but do look cool. I'd recommend that the authors learn more about verification, validation, and uncertainty quantification for fluid dynamics. And I'd encourage all machine learning folks approaching CFD to present your work at both fluids and machine learning conferences. I think problems like this would be reduced or fixed entirely by more interactions with fluid dynamicists.
Another smaller recommendation. What they call a "MAC grid" is called a staggered grid or mesh by CFD folks in my experience, so it might be better to use this terminology instead. The reference they cite is also out of date. I'd recommend something like this instead: https://www.sciencedirect.com/science/article/pii/S002199919...
This newer paper has higher order extensions of the method the 1965 paper uses and as I recall goes into much more detail about the properties of the schemes.
There are many recent works originating from the CFD community now. Too many to list here, you can PM me if you don't find them easily online for some reason.
