Panel methods offer numerous advantages for modeling inviscid, subsonic flows. For example, the flow solution is completely expressed
in terms of surface distributions over the solid walls and shed wakes, thus dispensing with the need for volumetric grids and the attendant mesh generation
difficulties. This feature is especially attractive for problems involving multiple bodies in relative motion such as store separation, propellers, flapping
mechanisms, etc. Another advantage is low numerical dissipation of shed wake structures allowing efficient and accurate long time simulations of helicopter
wakes and trailing wakes off aircraft wings. The chief drawback of panel methods is the quadratic growth in storage and CPU costs with element count. Thus
for N panels, costs grow in proportion to N2.
Fast multipole methods offer one venue for reducing these costs. These methods combine a hierarchical spatial partitioning strategy
(effected using octree data structures) and a multipole approximation to characterize the long range influence of a group of panels or wake elements, to achieve
O(NlogN) scalings in computation times and costs. In practice O(10) reductions in costs are typically achieved for N=2000.
Fast multipole technology has entered its way into CDI's CHARM code for modeling unsteady rotorcraft flows, a fast version of NASA's
PMARC-14 software and CDI's fast panel/vortex (FPV) code. FPV has been used in a variety of applications including: agricultural aircraft wake modeling for
spray drift assessment; aeroelastic modeling of flight vehicles; aircraft hover and take-off simulations on naval carriers to assess steam ingestion; submarine
wake modeling to examine methods for accelerating wake break up; simulation of ducted propulsors and the study of various flapping flight and propulsion concepts.
Some examples depicting the wake structure for a hovering JSF configuration, an impulsively started straked planform and a ducted propulser are shown below.
Wing shed vortices of a hummingbird. Please wait while movie is being loaded...
JSF configuration in hovering flight.
Start up wake for straked configuration.
Hydrodynamic wake shed from deflected ducted propulser.
3D wake generated by sinusoidally plunging AR=10 wing.
Comparison of the 3D shed wake with the 2D results from Jones (Jones, K. D., S. J. Duggan, and M. F. Platzer "Flapping-Wing Propulsion for a Micro Air
Vehicle." AIAA-2001-0126, 39th Aerospace Sciences Meeting & Exhibit, Reno, NV, 2001). This configuration produces a net propulsive force (CT=0.009).
Boschitsch, A. H., Usab, . & Epstein, R. J. (1999). Fast Lifting Panel Method. In 14th Computational Fluid Dynamics Conference (AIAA-99-3376, ed.), Norfolk, VA.
Boschitsch, A., Curbishley, T. B., Quackenbush, T. & Teske, M. E. (1996). A Fast Panel Method for Potential Flows About Complex Geometries. In 34th AIAA Aerospace
Sciences Meeting & Exhibit (A96-0024, ed.), Reno, NV W. J. J.