# Example of Units...

Hello Everyone,

I have documented a small example of converting from physical units to lattice units. Please find the file at this link

I am missing the Non-Dimensional part here.

Experts please correct me if I am doing something wrong…

Thanks in advance,
Narender Koosukuntla.

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.

Elrohir

You are a lifesaver, nkoosukuntla.
This forum was really missing a post like this.

Thanks a lot

Hello everyone,
based on nkoosukuntla’s file, I write a simple octave/matlab script http://dl.dropbox.com/u/7159543/conversion_units_lu_ph.m .
I hope it can be useful!

Greetings

Hi All,

Can anybody please post a similar conversion for pressure and density?

Thanks,
Narender

Yeh some one kindly doo it for pressure ad density…

Hi Narender,

YOur link is dead and I have lost my copy of it. Would it be possible for you to upload it again? I really need to re-consult with it. Many thanks!

Hi,

No problem. I will search in my documents and upload it.

Thanks,
Narender

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)

nu_lb = [delta_t / (delta_x)^2]*nu_d and nu_d = [t_p / (l_p)^2]*nu_p (kinematic viscosities)

P_lb = [(delta_t)^2 / (delta_x)^2]P_d and P_d = [(t_p)^2 / (l_p)^2][P_p / rho_p] (pressure)

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.

Regards,
Rohan

Hi all,

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.

C1 = L_p / L_lbm = 0.001
C2 = U_p / U_lbm = 100
Re = L_p * U_p / ν_p = L_lbm * U_lbm / ν_lbm = 100 so ν_lbm = (L_lbm * U_lbm) / 100 = 0.01 and ν_p = ( L_p * U_p ) / 100 = 1e-3

also, we have below equation
ν_p / ν_lbm = U_p / U_lbm * L_p / L_lbm or C3 = C2 * C1 = 0.1

ν_p = ( τ - 0.5 ) * Cs * Δt_p , Cs = 1/3 * Δx_p^2 / Δt_p^2 , C11 = Δx_p / Δx_lbm = Δx_p = 0.1/100 , C4 = Δt_p / Δt_lbm = Δt_p

therefore
ν_p = (( τ - 0.5 ) /3) * C11^2 /C4 , also ν_lbm = ( τ - 0.5 ) /3

C4 = C11^2 / C3 = 0.001^2 / 0.1 = 1e-5

Best Regards,

Hello arman3939,

I read your response. I coludn’t understand the following line:

ν_p = ( τ - 0.5 ) * Cs * Δt_p , Cs = 1/3 * Δx_p^2 / Δt_p^2 , C11 = Δx_p / Δx_lbm = Δx_p = 0.1/100 , C4 = Δt_p / Δt_lbm = Δt_p

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.

Can you explain it, please?

Thank you.

Regards,
Rohan