A Framework for Generating Radial and Surface-Oriented Regularized Stokeslets

Abstract

Error in the method of regularized Stokeslets is highly dependent on the choice of the blob or regularization function that is utilized to handle singularities in the flow. In this work, we develop a general framework to choose regularizations at the level of the vector potential via smoothing factors. We detail the derivation for radial smoothing factors and specify properties which ensure that the solution is a regularized flow satisfying the incompressible Stokes equations. Error analysis is completed for both the far-field flow (away from the location of the forces) as well as at the location of the forces, relating our newly derived smoothing factors to commonly used blob functions and moment conditions. When forces are on a surface, we extend the radial smoothing factor case to the case of non-radial regularizations that are surface-oriented. We illustrate the utility of this framework by computing the forward and inverse problems of a translating sphere using radial and surface-oriented regularizations.