micro-space flow

Dear every,

I am study the micro-space flow using Lattice Boltzmann Method now. And very confused about the relationship betwenn the relaxation time and knudsen number.
In my mind,
1.The relaxation time(tau) is calcualted from the viscosity first.
2. using equation tau’=0.5+1/density*(tau-0.5) to calculate the relaxation time that used into the code
3. using equation Kn=0.5*(tau-0.5)/(density*diameter). This Kn will be used to set the coefficient of the boundary condition.

Could you please help me to check this list is right.

And also , I read some papers and find that the Kn can equal to 1 and 10 , but if the Kn is so larger , the tau will larger than 2. I remember the tau is from 0.5 to 2. why the Kn can equal to so larger number.

Thank you very much for you answering.


Never worked with Knudsen scaling for rarefied flows. But, one comment - tau can be larger than 2, only omega=1/tau varies from 0 to 2.

Hopefully it will help,