Direct coupling between molecular dynamics and lattice Boltzmann method based on velocity distribution functions for steady-state isothermal flow

The direct coupling scheme between the molecular dynamics (MD) and lattice Boltzmann method (LBM) is established in this paper. Different from the existing coupling schemes which are based on the exchange of the density and velocities, the proposed coupling scheme is based on the velocity distribution functions. Firstly, the relations between the discrete velocity distribution functions of LBM and the continuous velocity distribution functions of MD are derived based on the Hermite expansions. Then, the coupling schemes between MD and LBM are proposed. The inconsistency between the equation of states of MD and LBM is specially treated and the deviatoric stresses are exchanged. The coupling simulations of the Poiseuille flow and Couette flow demonstrate that both the velocity and stress can be well exchanged by the coupling scheme. The coupling simulation of the flow past a nanotube shows that the proposed method can be further used in the study of microscopic fluid flow problems.