Slip boundary conditions in lattice Boltzmann simulations: On-site stress-tensor-based formulation

We propose a stress-tensor-based approach for fixing on-site hydrodynamic slip boundary conditions in lattice Boltzmann simulations. The formulation is presented in the framework of the widely employed D2Q9 lattice but it can be similarly applied to other lattice models. In our method, the slip length is a prescribed parameter and the Robin-type conditions to be enforced at an off-lattice wall point are transported to a wall-adjacent wet node and reinterpreted in terms of stress components. The resulting constraint equations at the wet node are solved by correcting inbound populations (whose reference values are given by the bounce-back rule) so that, along with the impermeable-wall condition, the desired relation between slip velocity and tangential stress is matched. The implementation is local and accounts for the effects of body forces, moving walls, and surface curvature; mass conservation is also ensured. Numerical tests reveal the scheme to be of satisfactory accuracy and it can therefore be regarded as a straightforward and easy-to-code alternative method for describing slippery boundaries in lattice Boltzmann simulations.