unit conversion D2Q9 VS D3Q19

Does somebody know if there are any difference between D2Q9 and D3Q19 in the algorithm of units’ convertion ?
I think that no, but above question is a reason of different results that I received in simulation even in simple tube when I compare physical velocity coming from LBM with velocity calculated directly from Poiseuille equation.


The unit conversions are the same. This of course can only be valid if the two simulations are “comparable”, e.g., using D3Q19 with z-extension = 1.