# Problem with small Reynolds Number

Hi guys,

so far i used Reynolds-numbers > 1, and everything looked like fine, but now i need to use Re < 1 and i get some weird results.

Here are my Input values:

I apply an external field, with deltaP_ex = 5 Pa/m, with an x-axis lenght of lx_p = 6.9E-4 m.
-> deltaP_p = deltaP_ex * lx_p = 3.5E-3

and my velocity in x-direction is therefore:

ux_p = sqrt (2*deltaP_p / rho_p) = 1E-3 m/s

with:
rho_p = 7000 kg/m³
lx_p = 6.9E-4 m
ly_p = 4E-4 m
lref = 4E-4 m
visc_p = 7.13E-7 m² /s
N = 200.

therefore i end up with a Reynoldsnumber Re = (ux_p * lref) / visc_p = 0.557 which is ok.

The above values lead to visc_lb = 7.17 (and also geLatticeNu() does).

With BGK-dynamics, tau = visc_lb/c_s² + 0.5 should be true (c_s = sound speed in the lb system), which leads to an tau = 22.093 and this looks like the reason for my problems.

But on the other hand, if I calculate the Mach number with Ma = ux_p / c_s
and use

Ma / Re = 1/sqrt(3) * (tau - 0.5) / N

I end up with

tau = 1.07

getTau() also produces the 22.093, so I guess the Ma of my System isnt the value I come up with from the above equation.

But where do I define it in palabos, or what else I am doing wrong ?

thx for any input,

Cheers,
Chris

Hi,

I’ve not been able to follow your calculations in detail, but here’s the big picture:

• Yes, a relaxation time of tau=22 is too big; tau should stay close to 1.
• Yes, If you decrease the Reynolds number while keeping constant the lattice-units velocity and grid resolution, then tau increases.
• A solution is to decrease the lattice-units velocity at the same rate as you decrease the Reynolds number. Then, the relaxation time tau stays constant and you’re fine.

Ok, so if I need a small Reynolds number, the rule of thumb for dt ~ dx², where dt = 1/N[sub]iter[/sub] and dx = 1/N does not apply here./?

So, i choose these values:

Re = 0.8 -> visc_d = 1.25
tau = 0.9

I calculated now the following:

with single BKG-dynamics, tau = visc_lb / c[sub]s[/sub][sup]2[/sup] + 1/2 leads to visc_lb = 4/3 E-1

now i use the relation between visc_d and visc_lb:

visc_d = (dx² * visc_lb ) / dt,

and dt = 8/3 E-6.

I picked N = 200, so dx = 5E-3 -> dt = 2.5E-5 is ~ 10 times larger than the dt from the above caluclation. Maybe the results are still ok with the larger dt.

But still, the tau from my original post was so high because I didnt decrease the lattice velocity.

So thanks again Jonas,

cheers Chris