A hybrid scheme coupling lattice Boltzmann method and finite-volume lattice Boltzmann method for steady incompressible flows

We present a new hybrid method coupling the adaptive mesh refinement lattice Boltzmann method (AMRLBM) and the finite-volume lattice Boltzmann method (FVLBM) to improve both the simulation efficiency and adaptivity for steady incompressible flows with complex geometries. The present method makes use of the domain decomposition, in which the FVLBM sub-domain is applied to the region adjacent to the walls, and is coupled to the lattice Boltzmann method (LBM) sub-domain in the rest of the flow field to enhance the ability of the LBM to deal with irregular geometries without sacrificing the high efficiency and accuracy property of the LBM. In the LBM sub-domain, a cell-centered lattice structure-based AMRLBM is used and, in the FVLBM sub-domain, the gas-kinetic Bhatnagar–Gross–Krook (BGK) scheme-based FVLBM is adopted to reduce the numerical dissipation and enhance the efficiency of FVLBM. Moreover, not like the conventional LBM and Navier–Stokes equation solver-based hybrid schemes, the present hybrid scheme combines two kinds of lattice Boltzmann equation solvers, that is, AMRLBM and FVLBM, which makes the present scheme much simpler and better consistency than the conventional hybrid schemes. To assess the accuracy and efficacy of the proposed method, various benchmark studies, including the Kovasznay flow, the lid-driven cavity flow with Reynolds number Re=100, 400, and 1000, and the steady flow past a cylinder with Re=20 and 40, are also conducted. The numerical results show that the present scheme can be an efficient and reliable method for steady incompressible flows.