Lattice Boltzmann Simulation of the Sedimentation of Elliptic Particles

The Lattice Boltzmann Method (LBM) has recently become a popular tool for simulating solid particle suspensions. Due to the method's affinity for handling complex boundary conditions on a stationary Cartesian grid, the LBM presents a promising alternative to more computationally expensive methods. We analyze the effectiveness of this method by comparing the LBM results to those of a finite element method for the case of elliptic particle sedimentation. Due to the moving geometry, the finite element method necessitates mesh regeneration, and projection of fluid variables from the old mesh to the new one at each time step. The LBM avoids these complications by virtue of its fixed grid. We examine several methods to implement the boundary conditions on the surface of the moving complex geometry. We also investigate the benefits and detriments of two methods to calculate the total force exerted by the fluid on the particle, i.e., the method of Momentum Exchange, unique to the LBM, and the method of Stress Integration. Then we implement the LBM to study some interesting phenomena associated with elliptic particle sedimentation. We analyze settling orientation, terminal Reynolds number, and frequency effects associated with shed vortices.