Fig 1.

(a) Typical non-uniform Cartesian mesh employed in the simulations. (b) Schematic of the control volume (not to scale) employed for the simulations and FPM. (c) Kinematics of the wing of the hovering hawkmoth and (d) fruit fly. In these plots, the trajectory of the leading edge of the wings at 2/3 span is identified by a thick line which is blue during downstroke and pink during upstroke. The chordlines at 2/3 span are also identified by black lines with circular “heads”. Time series of three characteristic angles (see inset in (f)) that define the wing kinematics for the (e) hawkmoth and (f) the fruit fly. For the hawkmoth, the instantaneous 3D wing shape and kinematics were quantified via high-speed stereo videogrammetry from recordings of the animal hovering steadily in front of an artificial flower [9]. For the fruit fly, a flat-plate wing was constructed from a high-resolution image of a fruit fly wing. Flapping kinematics consisting of three angular degrees of freedom were then extracted via high-speed stereo videogrammetry of a fruit fly, hovering shortly after takeoff, and imposed on the wing, resulting in rigid wing flapping kinematics. Fruit fly wings exhibit little deformation and the use of rigid wing kinematics is typical of mechanical [10] and recent computational [11–13] models of their flight.