Pressure Boundary condition at fluid solid interface


I am new to LBM. I am trying to apply pressure boundary conditions for a channel flow. I set the inlet density as 1.0005 and outlet as 1. However, the condition at the wall fluid interface is more tricky than I taught. From Sukorps book on page 53, the vertical velocity at north and south wall is calculated by an expression that divides the distribution functions by rho (Specifying the density (rho) to calculate velocity, this can also be seen to be the case in Zou and He’s paper on page 1593 equation 24). Does that mean I have to set rho to be a non zero integer. What could be a good value to choose as density at the north and south (upper and lower) plate given those inlet and outlet values? I will be happy even if one can tell me what boundary values to use for rho even if they are totally dfferent from the ones I am using, I just need workable values for the density at the solid wall. I believe the inlet and outlet is not much of a problem setting the density. I am using matlab for the simulation.