In Hybrid initialization, a Laplace equation is solved with appropriate boundary conditions to obtain the initial solution. The idea behind this is to obtain a good starting solution (at least better than what is given by the standard initialization). However, this equation does not take into account the effective properties of the porous media (which are scaled by the porosity). This is what the recommendation from the User Guide is referring to. For additional details, please refer to the following link on the theory guide.

If you are to use this, it is likely that you have a different starting solution for your run. That is about what I can comment on. I will not be able to comment on its closeness to the final steady-state solution as it is extremely dependent on the physics/models you are trying to solve. I've seen the solution go both ways - faster convergence or no convergence at all.

If you use Hybrid Initialization, only the initial solution does not account for the porous media properties. Once you start the run, the regular NS equations are solved and the correct properties are accounted during the calculation.

Regarding the boundary condition dependence - please refer to the theory guide link I shared.

I hope this answers your question.

Thanks.

Karthik