Macroscopic reconstruction of the lattice Boltzmann model for incompressible flows

The present work proposes a general framework that combines the good numerical stability of the lattice Boltzmann model for incompressible flows (LBM-IF) and the flexibility of finite difference/volume methods in using nonuniform meshes and removing higher-order deviation terms. By adopting the second-order non-equilibrium moment as fundamental variables and neglecting higher-order non-equilibrium moments, to approximately increase entropy in the collision process, the non-equilibrium-moment-based macroscopic equations of LBM-IF are derived. Numerical investigations demonstrate that discretized equations can achieve even better numerical stability than the single-relaxation-time LBM-IF. It is concluded that the good numerical stability of LBM-IF can be roughly interpreted as the entropy increase of the collision step and the diffusion process of the streaming step. However, the discretized non-equilibrium-moments-based macroscopic equations are found to have significant numerical errors at a fixed Reynolds number and very small kinematic viscosities. By combining the non-equilibrium-moments-based and equilibrium-moments-based macroscopic equations, the paper proposes a hybrid model that achieves good numerical stability and accuracy for both small and large kinematic viscosities, even for inviscid flow. The deviation term in the recovered momentum equation of LBM-IF can be easily removed in the hybrid model. Compared with LBM-IF, finite difference/volume solvers based on the hybrid model exhibit better numerical stability and accuracy, as well as superior efficiency in simulations using nonuniform meshes. © 2025 Elsevier Ltd.     «

The present work proposes a general framework that combines the good numerical stability of the lattice Boltzmann model for incompressible flows (LBM-IF) and the flexibility of finite difference/volume methods in using nonuniform meshes and removing higher-order deviation terms. By adopting the second-order non-equilibrium moment as fundamental variables and neglecting higher-order non-equilibrium moments, to approximately increase entropy in the collision process, the non-equilibrium-moment-bas...     »