Has anyone knows how to implement Slip boundary condition in LBM?
It depends on what kind of slip boundary you wish to implement.
If you know the slip velocity at a planar boundary, you could use any fixed-velocity (Dirichlet) boundary condition to apply that slip velocity along the wall (and a zero velocity orthogonal to it), such as Zou/He’s or Inamuro’s schemes.
If you wish to apply a free-slip boundary (i.e. no exchange of momentum tangential to the wall), you can use a specular reflective boundary condition, which is similar to the bounce-back condition that produces a no-slip boundary. While you would reflect the distribution function in the link orthogonal to the wall back the way it came, the diagonally travelling distribution functions would be sent forwards along the wall rather than being reflected back the way they came.
You can also combine this with the bounce-back condition to apply frictional slip and use coefficients to control how much of the flow is bounced-back and how much is reflected specularly. (This can also be related to setting a fixed velocity at the wall, although the above fixed-velocity schemes might be better in this case.)
I hope this is helpful.
Thank you so much for reply, sorry for so late reply. i was trying to do second situation that you explained ‘free-slip boundary (i.e. no exchange of momentum tangential to the wall)’. what do you mean by " diagonally travelling distribution functions would be sent forwards along the wall rather than being reflected back the way they came" , would you refer me to the book or paper that explain this method. Thanks in advance