A Vortex/Impulse Method for Immersed Boundary Motion in High Reynolds Number Flows

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. 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. The convergence of the method is demonstrated numerically. The method is then used to track the motion of an undulating filament, simulating the swimming of an organism in a slightly viscous fluid.