I am currently looking into the reasons for Tau dependency of the single particle settling velocities when using the BGK LBM D3Q15 method. From what I can gather the Multiple Relaxation Time methods do not have this problem. However I am finding MRT a little difficult to implemented in my code and so I am unable to test this at the moment.
What I wanted to ask is, why is there this difference between BGK and MRT? If anyone could recommend a good paper that deals with this issue I would very much like to read it!
Thanks for your reply. I guess it could be that, but I am not really sure why. It seems that boundary effects could be the reason for the settling velocity changing with Tau. I am using the immersed boundary method of Owen et al. (2010, http://onlinelibrary.wiley.com/doi/10.1002/nme.2985/abstract ).
What I see is that at a critical value (Tau = 0.85) the sphere falls at the terminal velocity predicted by Stokes’ equation and, to a reasonable level, grid resolution independence.
For values of Tau higher and lower than 0.85 the sphere falls at velocities higher and lower (respectively) than the Stokes’ prediction. Using a finer grid resolution moves these values closer to the ideal solution, but there is still a discrepancy.
It is not really the same situation but figure 1 in the paper of Li et al. (2005, http://pre.aps.org/abstract/PRE/v72/i2/e026705 ) shows the same sort of behaviour for flow through a porous media system and compares BGK with MRT. Is this difference between the results of these two methods due to the treatment of boundaries?