# Accelerated Lattice Boltzmann Method

## Abstract

The LBM is a powerful numerical fluid solver especially in the areas of multicomponent and multiphase 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. To increases the efficiency of the LBM and especially for multiphase flow simulations, the migrating multiblock (MMB) was introduced.

This chapter presents an extension scheme for the application of the single phase multiblock lattice Boltzmann method (LBM) to the multiphase Gunstensen and Shan and Chen models. The grid is refined for part of the domain where a fluid–fluid interface evolves, and the refined grid is free to migrate with the suspended phase in the flow direction. The method is applicable to single and multiphase flows in 2D and 3D domains. This accelerated scheme was demonstrated by simulating a benchmark single phase flow around a 2D asymmetrically placed cylinder in a channel and for investigating the shear lift of 2D neutrally buoyant bubble in a parabolic flow. The method was also used for simulating cases of 3D rising bubbles in infinite medium, in which the model results for the bubble terminal velocity were in good agreement with a semianalytical solution, and the produced shapes fitted very well in an experimental shape regime map. The MMB was also used for the study of the sedimentation of droplet onto horizontal surfaces with different wetting characteristics of wall surface, which led to the identification of three different regimes of droplet shapes. It was shown that the process of different regimes can be controlled by changing the wetting characteristics of surface.

## Keywords

Lattice Boltzmann Method Bond Number Fine Block Droplet Shape Fine Node## Supplementary material

MMPois. Phase field density contours show the migrating fine grid while tracking a moving droplet inside a channel (WMV 504 kb)

Vortex shedding. Vertical velocity contours for a multi-block simulation are shown here. (see Fig. 3.7) (WMV 246 kb)

MIGrho. Phase field density contours show a fine grid migrating along with the droplet in a 2D channel. The droplet is observed to move away from the wall towards the center of the channel due to the lift force acting upon it. (see Fig. 3.9) (WMV 303 kb)

MBouy1. 3D simulation of rising bubble of a rising bubble in infinite medium is shown for two different Eotvos numbers E_{o} = 374 [MBouy1] and E_{o} = 449 [MBouy2]. The movies show the migrating fine grid tracking the center of mass of the rising bubble and moving along with the bubble. (see Fig. 3.16 and Table 3.1) (WMV 255 kb)

MBouy2. 3D simulation of rising bubble of a rising bubble in infinite medium is shown for two different Eotvos numbers E_{o} = 374 [MBouy1] and E_{o} = 449 [MBouy2]. The movies show the migrating fine grid tracking the center of mass of the rising bubble and moving along with the bubble (see Fig. 3.16 and Table 3.1) (WMV 174 kb)

Trailing. 3D phase field contours of two trailing bubbles are shown in the movie. Movie shows the fine grid moving along the trailing bubbles (see Fig. 3.22) (WMV 247 kb)

3DSCMMBsed0. 3D phase field contour of droplet sedimenting under the influence of gravity is shown for pseudo-potential multi-component LBM model. The droplet and the fine grid migrate together to the bottom of the domain (WMV 146 kb)

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