You convert units while keeping the Reynolds number the same, which is ok, I think. But I wonder if you are really free in choosing the relaxation time tau. Maybe for incompressible flow you are, but I think that for compressible flow you would first have to set the time step delta_t = delta_x * cs/Cs with cs and Cs being respectively the lattice and physical speed of sound. Then calculate the lattice viscosity and from that the relaxation time.
I’m not an expert, but I think it should be like this.

Hi all,
I am also confused about unit conversions. But I have come up with conversions for pressure and in turn for density (reference http://wiki.palabos.org/_media/howtos:lbunits.pdf)…
delta_x = 1/ N where N is lattice resolution
delta_t ~ (delta_x)^2 OR we can back calculate it by assumming some value for ‘tau’ (relaxation time always >0.5)
from problem statement we can calculate ‘Re’
p -> physical , d -> dimensionless, lb -> lattice units
Now ,
u_lb = [delta_t / delta_x]*u_d and u_d = [t_p / l_p]*u_p (velocity)

we can use the relation -> (rho_lb)*((c_s)^2) = P_lb to find density relation. but in general for incompressible flows physical density value remains unchanged.

I am a new fellow to LBM field, I anyone find it reasonably correct ot if find any corrections please reply.

despite unit conversion in LBM is easy however it looks very difficult. let me to explain it with a simple example.
any numbers are dimensionless and they don’t have any meaning, but when we define them as a special units (for example SI units) then we would be able to measure them, for example, 1 in dimensionless calculation can be 1 m or 10 m or 0.000001 m .
in general we can say dimensional_number / dimensionless_number = C . also that equation is used to obtain conversion of units from one system to another.
in LBM for most cases (specially for simulating the incompressible fluid) we set Δt = 1 and Δy = Δx = 1 therefore the number of the nodes is equal to the length. for example N = 100 so L_lbm = N * Δx = 100.
according to the general equation, the physical characteristics is related to the LBM by
L_lbm * C1 = L_physical or C1 = L_physical / L_lbm.
C2 = U_physical / U_lbm
C3 = ν_physical / ν_lbm
and so on.

let me give you an example; the characteristics of length and speed in physical units are 0.1 m (= L_p) and 1 m/s ( = U_p) respectively. as well as, Reynolds number is equal to 100, length and speed in lattice units are 100 and 0.01. at first we obtain viscosity in lattice and physical units and then time in physical unit will be calculated.

I think, you refer τ (‘tau’) as relaxation factor. I didn’t find any relation in any of the literatures I reffered which relates τ with physical v_p (kinematic viscosity). Also the relations for C11 and C4 are confusing for me.