New lifting relations for estimating LBM distribution functions from corresponding macroscopic quantities, based on equilibrium and non-equilibrium moments

• New lifting relations are developed to construct a hybrid NS(FVM)-LBM(MRT) method.
• Hybrid method is implemented to a 3-dimensional problem for the first time (based on authors knowledge).
• Using new hybrid FVM-LBM (MRT) method to simulate flow around complex geometries such as porous media.

Due to superior accuracy and stability of multiple relaxation time (MRT) collision operator over its single relaxation time (SRT) counterpart, new lifting relations are proposed here to construct single particle distribution functions for MRT-LBM from macroscopic variables. Using these lifting relations, a new hybrid FVM-LB method is presented (called Finite type-LB hybrid method), which is consistent with MRT-LBM. In this new hybrid method, single-particle distribution functions in MRT-LBM sub-domain boundaries are computed, using equilibrium and non-equilibrium moments. These moments are computed in Navier–Stokes/FVM sub-domain boundaries, using macroscopic variables and their derivatives. The new method is validated by solving three benchmark problems, i.e., two- and three-dimensional lid driven cavity flows and two-dimensional unsteady flow around a squared section cylinder. These problems are analyzed with pure FVM, pure LBM, and Finite type-LB hybrid method (FTLBHM) and the related results are compared with each other and with benchmark data. These comparisons clearly demonstrate the accuracy of the present novel methodology for simulating steady/unsteady flow fields in two and three dimensions.