shear stress in LBM

Lattice Boltzmann Method LBM: Theory
#1

Hi every body.
i have written a simple code for 2D channel flow with an obstacle for a fluid with tau=0.7.
1-how can I calculate shear stress in LBM?( I need a reilable formula)
2- if i want to simulate nonnewtonian(such as powerlaw or careu-Yasuda) fluid what could i do?(As i konw in this case tau is not constant…)
3-my code is very sensetive to tau. for example if i change it to 0.5 or 0.52 program diverge. is there any problem in ht code or it is normal?
thanks

#2

Hello,

for your first question, you could start with this article.
There are some publications available for non-Newtonian fluids and LBM, e.g., this one.
Regarding your last question: It is well known that LBM does not work when tau is close to 0.5. Why are you such close to this limit? Do you simulate large Reynolds number flows?

Timm

#3

Thanks Timm
I get tau=0.7 in my program independet of reynolds. i implemet uniform velocity(U0) at inlet and fully developed flow at outlet. So if I relate Re to tau : Should i do these steps:
1- suppose known reynolds number
2- set: nu=U0H/Re (H:height of channel)
3-tau=3nu+0.5
shoud i follow steps mentioned above?

#4

It always depends on where you want to start. If, for some reason, your H and u are fixed, then tau is uniquely defined by the Reynolds number (as you describe it in your post). If, on the other hand, tau and u are fixed, then H is a function of the Reynolds number. At the beginning of your LBM research, it may be a bit challenging to set all the parameters in a range where they should be. In practice, H is limited by memory and computational load, u is limited by accuracy and number of time steps, and tau is limited by accuracy and stability. As long as all three parameters are in a “safe” window, it is not important whether you first set H and u or tau and u.