# about relaxation time and kinematic viscosity

Hi everybody,

I’m now studying single-phase & triple-component LBM and code is almost done, but I’ve got trouble about value of tau. In my code, tau is calculated by kinematic viscosity, and it is undeniably fact. Result of calculation with species property, values of tau are about 0.8, 1.03, 1.2(H2O, N2, O2, in order). With conditions that I concern, though, calculation reachs just 2195 steps and stop because of negative density value of N2.

I suddenly hit upon the paper which mentioned about tau that, “value of tau were set to be unity for stability”. I apply it to my code, now it works 75000 steps and still working, amazingly!!

So… my question is…
This is CORRECT?? If it is, why? Changing value of tau means that value of kinemativ viscosity become difference and will not equivalent with real property. Can it be suitable…?

best regard,
K. N. KIM

P.S.

1. Base of my model is paper of Luo and Girimaji[Phys. Rev. E 67, 036302(2003)] and McCracken and Abraham[Phys. Rev. E.71,046704(2005)]
2. I’m really thankful for this forum. Really helpful to me

So far I have only used the simple BGK-dynamics model with only one component, so it may be not exactly the same in your case.
But the principle idea should be the same, so If you take a look at tau:

tau = nu_lb / c + 1/2

with nu_lb = dt/dx^2 * nu_d and nu_d = 1/Re

tau = 3 * dt/dx^2 * 1/Re + 1/2

Now if you fix the values for tau (=1), and Re (or nu_d which comes from nu_ph), choose a value for dx (or the number of cells N, with dx=1/N), you are left with picking the right timestep dt, and nu_ph has still the value you wanted it to have.
Of course this usually means longer calculation time, but with the values you need.

nu_lb … viscosity in LB-units
nu_d… dimensionless viscosity
nu_ph… physical visc.
Re… Reynoldsnumber
dt… timestep LB
dx… grid spacing LB

hope that helps a bit^^