Calibration of the method of images for regularized Stokeslets using sphere motion near a boundary

Many numerical simulations in fluid dynamics require modeling a sphere in motion near a boundary. In Stokes flow, the method of images for regularized Stokeslets (MIRS) has been widely used and validated with theoretical results for the rotational and translational motions of spheres parallel or perpendicular to a boundary, respectively. Our work, taking into account all possible motions of a unit sphere, presents a systematic study that calibrates the MIRS with the theory and dynamically similar experiments. We find that the surface discretization called spherical centroidal Voronoi tessellations (SCVT) is the most accurate and robust for all motions when the point distribution on the sphere's surface is no longer symmetric with respect to the boundary. Our tests for popular surface discretizations using spherical coordinates or projection of points on a cube to a sphere (6-patch) show that they can only be used when symmetry, with respect to the boundary, is guaranteed. We also find a constant ratio, for all motions, of the optimal regularization parameter in free space to the inverse of the square root of the number of points used in SCVT. Our ongoing study will reveal if the discretization errors, optimal regularization parameters, and constant ratio are still the same if we change the regularization function in the MIRS.