Finding optimal computational parameters for the method of images for regularized Stokeslet

Many numerical simulations in Stokes flow require modeling a sphere in motion near a boundary. Since the method of images for regularized Stokeslets (MIRS) has been widely used for this purpose, we develop a systematic way to calibrate the MIRS with theoretical formulations (when they exist) and dynamically similar macroscopic experiments. Our work in 2021 calibrated the discretization sizes and regularization parameters in the MIRS using torques on cylinders and helices of different wavelengths as they rotated in a viscous fluid at various distances from a boundary. Using the same approach, our present work focuses on forces and torques of spheres moving near a boundary.

We discover that the surface discretization called spherical centroidal Voronoi tessellations (SCVT) is the most accurate and robust for all motions when we compare SCVT with discretizations whose point distributions on the sphere’s surface are symmetric with respect to the boundary. Depending on which regularization function is used in the MIRS, we find a constant ratio, for all motions, of the optimal regularization parameter in free space to the average distance used in the SCVT discretization. Our study reveals how the discretization type and size, optimal regularization parameter, and regularization function affect the accuracy and robustness of sphere-motion simulations.