A hybrid numerical scheme based on coupling discrete-velocities models for the BGK and LBGK equations

A hybrid method based on coupling of the model kinetic (BGK) and lattice Boltzmann (LB) equations is considered. The computational domain in the physical space is decomposed into the non-equilibrium region, where the discrete-velocity (DV) method is employed, and the near-equilibrium one, where LB modeling are applied. The matching conditions on the boundary between these subdomains are derived from the Gauss–Hermite quadrature. Several LB models including high-order lattices are considered. The test problem solution shows good accuracy and efficiency of the proposed algorithm.