LBM lattice logic


I have a simple (I think) but very persistent question and one that keeps popping up from time to time to annoy me!

Let’s imagine for simplicity that one needs to run a 2D simulation with D2Q9 lattice. In this scenario, how is term neighbouring node defined? Is it similar to figure 1 or to figure 2 For me the problem arises at the fact that the distance between the dots in both figures is by definition 1 lu and c (or e, depending on notation) is 1lu/ts. However when the streaming process takes place, the distributions are streamed let’s say from direction 1 on node x,y to direction 1 on node x+1,y, which suggests that a distance of 2 lu has been covered in one time step.

Thank you to all who share thoughts,