Flapping Wing Coupled Dynamics in Lie Group Setting

In order to study dynamics of flapping wing moving in ambient fluid, the geometric modeling approach of fully coupled fluid-solid system is adopted, incorporating boundary integral method and time integrator in Lie group setting. If the fluid is assumed to be inviscid and incompressible, the configuration space of the fluid-solid system is reduced by eliminating fluid variables via symplectic reduction. Consequently, the equations of motion for the flapping wing are formulated without explicitly incorporating fluid variables, while effect of the fluid flow to the flapping wing overall dynamics is accounted for by the added mass effect only (computed by the boundary integral functions of the fluid density and the flow velocity potential). In order to describe additional viscous effects and include fluid vorticity and circulation in the system dynamics, vortex shedding mechanism is incorporated by enforcing Kutta conditions on the flapping wing sharp edges. In summary, presented approach exhibits significant computational advantages in comparison to the standard numerical procedures that - most commonly comprise inefficient discretization of the whole fluid domain. Most importantly, due to its 'mid-fidelity' computational efficiency, presented approach allows to be embedded in the 'automated' optimization procedure for the multi-criterial flapping wing flight design.