Question on Lattice Boltzmann method
 

Hi I am still learning about LBM. However one thing that confuses me is the physical speed and sound speed. For the lattice sound speed cs=1/sqrt{3}, does it correspond to the physical sound speed for isothermal flow (sqt{RT}) ? If it does, then why isn't the physical speed (e.g. inlet speed of lid cavity) up converted accoringly? Like for instance,

cp=sqt{RT}≈330m/s --> cs=1/sqrt{3}≈0.5774
Then why isn't the physical speed u map accordingly
e.g. physical speed of inlet(lid) is up=0.2m/s --> converted to ul=0.3*0.5774/330

Instead the physical speed up is used together with the lattice speed of sound cs in the flow equilibrium distribution.

I may have miss something but for now I am really stuck at this part.