  In this paper, analytic relations between the macroscopic variables and the
mesoscopic variables are derived for lattice Boltzmann methods (LBM). The
analytic relations are achieved by two different methods for the exchange from
velocity fields of finite-type methods to the single particle distribution
functions of LBM. The numerical errors of reconstructing the single particle
distribution functions and the non-equilibrium distribution function by
macroscopic fields are investigated. Results show that their accuracy is better
than the existing ones. The proposed reconstruction operator has been used to
implement the coupling computations of LBM and macro-numerical methods of FVM.
The lid-driven cavity flow is chosen to carry out the coupling computations
based on the numerical strategies of domain decomposition methods (DDM). The
numerical results show that the proposed lifting relations are accurate and
robust.
