Simulating the dynamics of flexible bodies and vortex sheets

We present a numerical method for the dynamics of a flexible body in an inviscid flow with a free vortex sheet. The formulation is implicit with respect to body variables and explicit with respect to the free vortex sheet. We apply the method to a flexible foil driven periodically in a steady stream. We give numerical evidence that the method is stable and accurate for a relatively small computational cost. A continuous form of the vortex sheet regularization permits continuity of the flow across the body’s trailing edge. Nonlinear behavior arises gradually with respect to driving amplitude, and is attributed to the rolling-up of the vortex sheet. Flow quantities move across the body in traveling waves, and show large gradients at the body edges. We find that in the small-amplitude regime, the phase difference between heaving and pitching which maximizes trailing edge deflection also maximizes power output; the phase difference which minimizes trailing edge deflection maximizes efficiency.