Modeling slender bodies with the method of regularized Stokeslets

The motion and flow generated by immersed structures in a fluid in the Stokes regime can be modeled with a variety of different numerical methods. The mathematical structure of the Stokes equations allows one to describe the flow around a three-dimensional object using only information regarding its geometry. This leads to computational techniques such as boundary integral methods or the method of regularized Stokeslets that discretize the surface of the immersed object in the flow. However, when the body in question is slender, a more computationally efficient alternative is to represent the flow by a one-dimensional discretization along the centerline of the object rather than a discretization of the boundary. Using an exact and an asymptotic solution describing the nontrivial three-dimensional fluid flow generated by a slender precessing spheroid, we present a careful analysis of the approximation of the flow using the method of regularized Stokeslets, where the regularized Stokeslets are placed along the centerline of the spheroid. Guidance is presented on how best to choose the numerical parameters within the method of regularized Stokeslets to minimize the error for a given application.