Moving boundary conditions

MER

Hi, I have seen in different works related to multiphase flows that researchers use a non-inertial fram when modeling phenomena with transient boundary conditions and others make an integration of variables (velocities..) in time and stop the process of computation when these variables reach the zero value.

1) How can I calculate the added term in the momentuum (acceleration) and transport equations for the first case?

2) Is there any criteria when working with the second method?

thanks a lot.