dear

for example, you can treat different slip conditions using an Immersed boundary method. You can then impose simple Dirichlet boundary conditions to simulate various wetting or slip conditions at the wall. It may be quite computationally expensive depending on the number of Lagrangian points to simulate the wall but it is quite efficient.

Dear Dr. Poncet,

Thank you very much...

check this article (I think it is a simple scheme)

Long-Sheng Kuo, Ping-Hei Chen, A unified approach for nonslip and slip boundary conditions in the lattice Boltzmann method, Computers & Fluids, Volume 38, Issue 4, April 2009, Pages 883–887

If you are interested in it I can send you our paper

M.F. Uth, H. Herwig: A partial slip boundary condition for the Lattice-Boltzmann Method, Proc. of the Int. Conf. on Nano-, Micro-, and Minichannels, Sapporo, Japan, June 16 – 19, 2013, ICNMM2013-73026, 2013

Maxwell slip model, DSBC slip model, Longmuir slip model

I simulated some benchmark flows with these slip models.