Three-dimensional immersed boundary conditions for moving, solids in the lattice-Boltzmann method

This paper establishes the range of validity for a previously published three-dimensional moving solid boundary condition for the lattice-Boltzmann method. This method was reasonably formulated from a mass and momentum balance perspective, but was only verified for a small range of (primarily two-dimensional) problems. One of the advantages of this boundary condition is that it offers resolution at the sub-grid scale, allowing for accurate and stable calculation of the force and torque for solids which are moving through a lattice, even for small solid sizes relative to the computational grid size. We verify the boundary condition for creeping flows by comparison to analytical solutions that include both the force and the torque on fixed and moving spheres, and then follow this with comparisons to experimental and empirical results for both fixed as well moving spheres in inertial flows. Finally, we compare simulation results to numerical results of other investigators for the settling of an offset sphere and the drafting-kissing-tumbling of two sedimenting spheres. We found that an accurate calculation of the collision-operator weighting used to obtain sub-grid-scale resolution was necessary in order to prevent spikes in the velocities, forces, and moments when solid objects cross-computational cells. The wide range of comparisons collected and presented in this paper can be used to establish the validity of other numerical models, in addition to the one examined here. Published in 2007 by John Wiley & Sons, Ltd.