Lagrangian Vortex/Impulse Method by Ricardo Cortez
A Lagrangian method that combines vortices and impulse elements (vortex dipoles) is introduced. The applications addressed are flows induced by the motion of thin flexible boundaries immersed in a two-dimensional incompressible fluid. An example is an undulating filament simulating the swimming of an organism in a slightly viscous fluid. The impulse elements are attached to the boundaries and are used to account for the forces affecting the motion. The vortices occupy a region surrounding the boundaries and are used to account for the viscous effects via a deterministic diffusion method.

Regularized Stokeslets by Ricardo Cortez
This is a numerical method for computing Stokes flows in the presence of immersed boundaries and obstacles. 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.