difference between physical density and rho in LB

Hi every body
I have an essential question that confused me!
I want to analyze water flow in 2D channel with LBM. we know that density of water is 1000 kg/m3. and with this density we can calculate tau(or omega) in our program.
But what rho=sigma( fi) in program means? what is the difference between this rho and density of water(=1000 that is constant in this example)? I mean that if we calculate rho(y,x) for all domain at the end of program are they equal to density=1000??

sombody please help!

I do not get what you exactly want. But you should read the threads about unit conversions in LBM. Just search for “unit” or “units” and read a bit.