Simulation of Sedimentation of a Sphere in a Viscous Fluid Using the Lattice Boltzmann Method Combined with the Smoothed Profile Method

Abstract

We conducted a numerical study on the motion of a solid sphere settling under gravity in a viscous fluid using the lattice Boltzmann method combined with the smoothed profile method (SPM). The coupling of lattice Boltzmann fluid and a spherical particle is treated by introducing a body force term to the Boltzmann kinetic equation. For verification, we applied our numerical code to the simulation of flow over a static sphere and compared the results with previously published data. Later, we simulated the sedimentation process of a sphere inside a closed container. Our simulation results of the sphere's settling velocity and fluid velocity contours at various Reynolds numbers are in good agreement with the corresponding experimental results. Finally, we analyzed the accuracy of the present SPM for different forms for the smoothed profile function at various interface thicknesses and grid sizes.