Slip-flow boundary condition for straight walls in the lattice Boltzmann model

Abstract

A slip-flow boundary condition has been developed in the lattice Boltzmann model combining an interpolation method and a simple slip boundary condition for straight walls placed at arbitrary distance from the last fluid node. An analytical expression has been derived to connect the model parameters with the slip velocity for Couette and Poiseuille flows in the nearly continuum limit. The proposed interpolation method ensures that the slip velocity is independent of the wall position in first order of the Knudsen number. Computer simulations have been carried out to validate the model. The Couette and Poiseuille flows agree with the analytical results to machine order. Numerical simulation of a moving square demonstrates the accuracy of the model for walls moving in both the tangential and normal directions.