Computing Insect flight, Falling Paper, and Hydrodynamic Interactions.
Jane Wang (MAE)

The unsteady aerodynamics of insect flight and falling paper is governed by the Navier-Stokes equation subject to the movement of dynamic boundaries. The typical Reynolds numbers are on the order 100-1000, thus the fluid dynamics lies in the intermediate regime where both the viscous and inertia effects are important. Interesting physics in these kinds of problems often comes from the dynamic interaction between the moving objects and the fluid. Visually, this manifests in the formation of the vortices, which results from the separation of boundary layers. The strength of those vortices are critical for understanding part of the aerodynamic forces.

To solve this family of problems, we have worked on two classes of computational methods. One is a fourth-order finite difference scheme that is tailored to a single flapping wing problem, where we can find elegant solutions to resolving the sharp edges and far-field boundary conditions. The other is a more generally applicable method based on the idea of immersed interface method, which can be employed to simulate arbitrary number of rigid and flexible objects. One improvement over other similar methods is the resolution along the sharp interface. This follows from the derivations and implementation of the proper jump conditions satisfying the Navier-Stokes equation.

I will discuss both methods.