Multiphase with high density ratio


I am quite new to LBM and I’m trying to simulate a multiphase problem with water and air. As far as I’ve read, Shan-Chen approach is not valid due to the high density ratio. I have seen other topics on this matter in the forum, but it is not clear to me how I can handle this problem. Also, Palabos VOF-based multiphase model handles this problem, but I don’t know how it works, any documentation describing it? Can anyone refer me to some literature dealing with these topics? Thank you.