# problem with real/physical velocity

Hello Everyone,
I have had a problem even since 4 months.
In all my calculations by 3D LBM I always receive velocites divided by 1000.
To be more precise, I coded LBM D3Q19, and always velocity from LBM algorithm is about 1000 times smaller than real velocity (i.e. from reality).
I calulcate the physical velocity from LBM results in such a way:
v = sqrt( sum_e * sum_e + sum_t * sum_t * f + sum_n * sum_n)
where
sum_e = (f_e + f_ne + f_se + f_te + f_be - f_w - f_nw - f_sw - f_tw - f_bw) / density;
sum_n = (f_n + f_ne + f_nw + f_tn + f_bn - f_s - f_sw - f_se - f_ts - f_bs)) / density;
sum_t = (f_tc + f_te + f_tn + f_tw + f_ts - f_bc - f_be - f_bn - f_bw - f_bs)) / density;
density = sum of all lattice velocites

and next I multiply v by factor dx_ph/dt_ph
I checked many many times units and all translations look good.
Maybe somebody has any ideas, maybe I make a mistake in the above calculations?

Thanks for any help.

Hello,kjurczuk

The calculation seems no problem, the velocity you got is in lattice units. That is, velocity(lattice) is not equal to the velocity(phy), since
v(latt)=v(phy)/C. Thatâ€™s the way it should be.

So what do you want to say here?

Hello
Thank you for your interest.
Obviously I also used translation from lattice to physical units, as You said C = dx_latt / dt_latt
My question is, if other calculations that I make are good, when I calculate physical velocity from lattice velocities, I paste the calucaltions once again with adding the translation from lattice units to physical units.

v_phys = sqrt( sum_e * sum_e + sum_t * sum_t + sum_n * sum_n) * dx_latt / dt_latt
where
sum_e = (f_e + f_ne + f_se + f_te + f_be - f_w - f_nw - f_sw - f_tw - f_bw) / density;
sum_n = (f_n + f_ne + f_nw + f_tn + f_bn - f_s - f_sw - f_se - f_ts - f_bs)) / density;
sum_t = (f_tc + f_te + f_tn + f_tw + f_ts - f_bc - f_be - f_bn - f_bw - f_bs)) / density;
density = sum of all lattice velocites

maybe I should also add some multipliers sqrt(2) and sqrt(3) because of projection eg. f_ne to east direction, but I think that this multipliers are included in the LB model,

Thanks for any help