Migrating multi-block lattice Boltzmann model for immiscible mixtures: 3D algorithm development and validation

The lattice Boltzmann method (LBM) has emerged as a powerful numerical fluid solver especially in the areas of multi-component and multi-phase mixtures. However the LBM uses the particle velocity for the determination of the model time step required by the Courant-Friedrichs-Lewy (CFL) stability condition. This degrades the LBM efficiency, when compared with standard CFD solvers which use instead the macroscopic velocity for the CFL requirements. This paper discusses the development and validation of a 3D migrating multi-block model aiming at the acceleration of the LBM solution. The proposed algorithm is especially applicable to the Gunstensen multi-component model, in which a fine grid block engulfs the fluid-fluid interface and migrates with it. This increases the efficiency of the LBM since less iteration steps are required in areas of marginal interest, and it enables a better interface resolution because the fluid interface is always covered with finer grid. The method was demonstrated by simulating the case of a 3D rising bubble in infinite medium, in which the model results for the bubble terminal velocity were in good agreement with a semi-analytical solution, and the produced shapes fitted very well an experimental shape regime map.