[Mathematician]

I read some posts saying that the gravity has no effect on a single phase incompressible fluid since there is no variation of local density.

But if a fluid is at a certain height, the gravity source term should accelerate the fluid downwards, right? If I have a fluid on the moon, the fluid is just single phase, still it's going to accelerate.

Another question; If I have an eulerian incompressible FVM solver, how could I do the simulation lagrangian? (the fluid starts to fall from a certain height and then it reaches the ground, a problem that seems tricky to be solved with eulerian)

[sbaffini]

If we split density in a constant + variable part, the gravity term with the former can be absorbed in the pressure, which means that your whole domain has a base acceleration and resulting pressure gradient, but no relative motion comes out from that.

Relative motion due to gravity, instead, requires non constant density in space.

I try to interpret what you wrote and I guess you refer to liquids falling trough air, which indeed have different densities. Air would fall trough other air only if it is colder (with higher density) than surrounding air

[sbaffini]

I have now read some of your previous posts and better understand what you meant.

Vacuum is outside the validity limit of Navier-Stokes equations. Matter moving in vacuum under the influence of gravity is a completely different topic, that only under certain conditions can be retraced back to some form of fluid dynamic behavior.

[aerosayan]

Originally Posted by sbaffini

I have now read some of your previous posts and better understand what you meant.

Vacuum is outside the validity limit of Navier-Stokes equations. Matter moving in vacuum under the influence of gravity is a completely different topic, that only under certain conditions can be retraced back to some form of fluid dynamic behavior.

I've also seen the continuum assumption break down for partial vacuum, or rarefied gases.

In SU2-Nemo's conference videos for Martian atmosphere re-entry, they say that results from Navier-Stokes are not exactly correct.