Regularizing Stokeslets via "Brute Force"

The method of regularized Stokeslets is a powerful method for simulating low-Reynolds-number fluid flows, which has proven useful for describing, e.g., the locomotion of microorganisms. However, the method requires one to choose an appropriate regularization of the (singular) fundamental solution to the Stokes equations (the 'Stokeslet'). Typically, the Stokeslet is regularized by spreading the associated point force on the fluid with a smooth distribution and solving the resulting forced Stokes equations for the resulting flow. Here, we instead employ the vector potential associated with the singular Stokeslet and replace, by "brute force", the singular factor with regularized approximations. The resulting regularized Stokeslets are automatically divergence-free and may be chosen to have various desirable properties. For example, we may generate regularized Stokeslets that can be used with known hydrodynamic image systems in various geometries with low error, allowing (near) exact satisfaction of certain boundary conditions. Our regularization method is verified with results for well-known problems such as flow due to the motion of a rigid cylinder/sphere and of thin, flexible filaments.