Inamuro decoupled multi-phase model

Right so I’ve got a good grasp of one of the common methods of modelling two-phase flow as described in “LBE: an introduction to geoscientists and engineers”

My problem is that I am modelling vapor/water phase transition which has a density ratio of ~1000 for which the forementioned model is uncapable of reproducing. I found an article by Inamuro “LBE methods for viscous fluid flows and for two-phase fluid flows” which proposes using two distribution functions for recovering “phase ratio” and velocity/pressure.

Has anyone here implemented this or know of any examples of this? I am having problems understanding how some coefficients are evaluated so if anyone has experience of this I would love to ask some questions.