Modeling nano scale flow with lbm

I am working on modeling of flow through Mems.durimg my studies, I found it impressive.I mentioned here the most recent update model that i have found but i am not sure that this model is working properly.

DOI: 10.1007/s10955-005-8416-9
Journal of Statistical Physics, Vol. 121, Nos. 1/2, October 2005 (© 2005)
Gas Flow in Microchannels – A Lattice Boltzmann
Method Approach
Y.H. Zhang,1 R.S. Qin,1 Y.H. Sun,1 R.W. Barber,1 and D.R. Emerson1

Please put here the most recent update model.I think this model is good, because of the modification of relaxation time and boundary condition.

But there is a problem here, as you know when the knudsen number is high the total density variation through the duct is also high…Does it trigger to mutiphase flow??
what is your comment??
thank you