Incompressible multi-relaxation-time lattice Boltzmann model in 3-D space

Multi-Relaxation-Time Lattice Boltzmann Method (MRT LBM) is of better numerical stability and has attracted more and more research interests. The previous MRT LBM included artificial compressible effects. To overcome the disadvantage, an incompressible MRT LBM has been proposed in two dimensions recently. In this article, we present incompressible MRT LBMs in 3-D space, with example of nineteen-velocity. The equilibria in momentum space are derived from an earlier incompressible Lattice Bhatnagar-Gross-Krook (LBGK) model proposed by Guo et al. Through the Chapman-Enskog (C-E) expansion, the incompressible Navier-Stokes (N-S) equations can be recovered without artificial compressible effects. Simulations of a lid-driven cavity flow in three dimensions with Re = 1 000, 2 000 and 3 200 are performed. The simulation results agree with the existing data and clearly demonstrate better numerical stability of the presented model over the incompressible LBGK model.