“If needed you can cut off them by setting values smaller than zero to zero.”

I agree that if these negative values are close to 0, a cutoff can be applied to rectify the problem. However, these negative values are not small compared to the physical limits of the volume fraction field. In the “fallingDrop3d” example, you can observe values of -4.6 and -5.3 for the second and third written steps when viewing the results in Paraview. Later in the simulation, the negative values start getting smaller and closer to zero.

In the verification example I am working on, rising of a single bubble in a column of liquid, the negative values remain far from zero, -8 to -12, for the entire simulation.

” Does that course problems?”

Unfortunately, I did not understand this part of your answer.