Reply To: Low Density Simulation
the relation between density and pressure you mentioned is correct and holds in this context for the LBM considering the respective equation of state. A proper derivation can be found in many LBM related literature (e.g https://www.springer.com/de/book/9783319446479).
Setting a specific characteristic physical pressure, however, is not solely an LBM related issue. As the compressible/slightly-compressible Navier-Stokes equation does not include the absolute pressure, but only the pressure gradient, changing the default value does not have any effect on the fluid flow solution (despite, obviously the resulting absolute pressure). As this is a matter of general fluid dynamics, you might want to have a look at respective literature for further insights.