shear stress in LBM

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?


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?


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)
shoud i follow steps mentioned above?

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.