The Method of Regularized Stokeslets

Abstract

A numerical method for computing Stokes flows in the presence of immersed boundaries and obstacles is presented. The method is based on the smoothing of the forces, leading to regularized Stokeslets. The resulting expressions provide the pressure and velocity field as functions of the forcing. The latter expression can also be inverted to find the forces that impose a given velocity boundary condition. The numerical examples presented demonstrate the wide applicability of the method and its properties. Solutions converge with second-order accuracy when forces are exerted along smooth boundaries. Examples of segmented boundaries and forcing at random points are also presented.