Bridging the Lattice Boltzmann Method and Moment Methods

Abstract: We derive discrete moment equations exactly equivalent to the lattice Boltzmann method (LBM) and identify the general moment closure shared by kinetic methods based on the discrete-velocity Boltzmann equation. This closure provides a route to correct lower-order dynamics without requiring accurate reconstruction of the higher-order moments, thereby substantially broadening the scope of existing closure strategies that seek increasingly accurate representations of these moments. These advances establish a unified moment framework bridging LBM and moment methods. The framework enables efficient simulations across all Knudsen regimes, overcoming the prohibitive complexity of existing moment methods at high Knudsen numbers. It further provides a common basis for integrating and extending key features of diverse kinetic methods.