Boundary conditions with adjustable slip length for the lattice Boltzmann simulation of liquid flow

The phenomenon of liquid slip has been studied by many researchers using the lattice Boltzmann method. However, boundary conditions for the lattice Boltzmann simulation of liquid flow are far from perfect and how to specify the boundary conditions for liquid flow with slip accurately is still a challenge. In this work, we introduce four widely used slip boundary conditions in gaseous flow into the simulation of liquid flow, two half-way schemes and two modified schemes. Theoretical analysis shows that all half-way schemes are equivalent in principle, so are the modified schemes. According to the equivalence of these schemes, these slip boundary conditions are improved by expanding the range of the combination parameters from [0,1] to [0,2] to surmount the barrier of limited simulated slip length. And the relations between the combination parameters and the slip length are deduced strictly in theory. The specified combination parameter is decided by the given slip length and the relaxation time. The discrete effects of these slip boundary conditions are analysed. If the grid is fine enough, the discrete effects can be ignorable and the local flow at the wall can be approximated as flow with linear velocity gradient. The accuracy and reliability of our method have been verified by the simulations of the Couette flow, the Poiseuille flow and the unsteady Womersley flow. The cylindrical Couette flow is also implemented to explore the possibility of simulating liquid flows with curved boundary