formulation of the inamuro non slip boundary condition (Inamuro boundary conditions)

Hi every one,

I am trying to derive the formulas for the implementation of the nonslip boundary condition by Inamuro et al (A non slip boundary condition for LB simulations, 1995) in 2D. I was able to derive the one for wall density as stated on page 2929 of the paper (in 2D). However, I have not been able to get the right formulas for the rho prime and u prime. I think its a problem with my formulation of the equations. I looked up for more insight in Succi’s book (page 88), The Lattice Boltzmann equation for fluid dynamics and beyond. I could still not get the right formulas. I wish to extend the conditions to 3D boundaries.

Is any one able to help on the right equations I am supposed to solve to be able to get the counter slip velocity and rho prime?

I tried to solve the equations below for rho prime and u prime.
RhowUw+RhowVw=Rho’ * U’…eqn1

Its a bit difficult typing it here, but
Rhow=density at wall
Uw=x component of wall velocity
Vw=y component of wall velocity
U’=counter slip velocity
Rho’=unknown density

Thanks very much for anticipated help