A fast panel method for potential flows about complex geometries
Alexander H. Boschitsch, Thomas B. Curbishley, Todd R. Quackenbush, Milton E. Teske · 34th Aerospace Sciences Meeting and Exhibit · 1996
The panel method remains one of the most widespread and commonly used techniques for aerodynamic analysis and design. One of its most appealing properties is that no volumetric grid is required; only the bounding surface must be discretized. Compared to the generation of a good quality volumetric grid, construction of a surface mesh for a complex geometry constitutes a far simpler problem especially since the required geometric information is often already available in the form of CAD files and robust and efficient grid generation techniques for curved surfaces have been developed. Unfortunately, the simplicity afforded in grid generation and economy in the number of panel elements is offset by a quadratic growth in both CPU and storage costs with the number of panels which results from the fact that each panel exerts influence upon every other. This paper describes a novel 'fast panel' implementation which alleviates this computational burden. By combining hierarchical grouping techniques based upon octree structures and formal multipole/Taylor series expansion approximations, both storage and CPU costs are reduced to O(N). An iterative solution procedure is adopted (to minimize storage) in conjunction with the generalized minimum residual (GMRES) method to accelerate convergence. Examples of flows over complex geometries involving more than 104 panels are presented and shown to converge within several minutes on a Silicon Graphics Indigo work station.