I want to simulate the Poiseuille flow in a duct where the inlet velocity is equal to v_max = 0.02 m/s.
The hight of the model is 0.05 m and the estimated Reynolds number is Re ~ 1000
I am planning to divide the height in 100 lu so 1lu = 0.0005 m
How do I calculate the inlet lattice velocity?
From the channel dimension, the Reynolds number and the velocity you can first compute the viscosity nu,
Re = d * v / nu (or however you define your Reynolds number)
From nu and dx (your lattice resolution), you get the time step dt, if you know the relaxation parameter tau:
nu_L = (tau - 1/2) / 3,
nu_P = nu_L * dx^2 / dt,
where the index L indicates lattice quantities and P physical quantities.
Having dx and dt (in meters and seconds, respectively), you can compute the lattice velocity:
v_L = v_P * dt / dx.
This is in principle all you have to do.
Please be aware of the fact that you have three degrees of freedom: lattice resolution dx, time step dt (or relaxation parameter tau) and velocity v (or Reynolds number). You have to set all three of them in order to run your simulation in a well-defined way.
it is not very easy to find clear literature regarding this topic. I think that everybody has to find his/her own way to set up the LB parameters correctly. It took me some time to understand how to find good parameters values. You may have a look at our recent paper here (esp. section II F and IV B), but I do not believe that it will answer all of your questions. However, you can have a look at the cited references.