A lifting relation from macroscopic variables to mesoscopic variables in lattice Boltzmann method: Derivation, numerical assessments and coupling computations validation

► Analytic relations between the macroscopic variables and the mesoscopic variables are derived for lattice Boltzmann methods. ► The properties of the reconstruction operator are investigated by the numerical researches. ► The effect of the mesh size on the accuracy of the reconstruction operator is presented. ► The proposed reconstruction operator is used to implement the coupling computations of LBM and macro-numerical methods of FVM. In this paper, analytic relations between the macroscopic variables and the mesoscopic variables are derived for lattice Boltzmann methods (LBMs). 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 (DDMs). The numerical results show that the proposed lifting relations are accurate and robust.