Abstract
In this paper, a new approach is presented for calculating the incompressible flow around a three-dimensional lifting body by modeling the body surface as a vortex sheet, as opposed to source and doublet distributions typical of traditional panel methods. The vortex sheet is represented by triangular panels with linearly varying surface vorticity, resulting in a second-order rate of convergence with respect to panel refinement. Surface vorticity is determined by enforcing flow tangency constraints at each triangle centroid, zero circulation around each panel perimeter, and the unsteady pressure matching Kutta condition. These constraints result in an overdetermined system that is solved in a least-squares formulation. This surface vorticity method is validated against the analytical solution to the potential flow around an ellipsoid, and it demonstrates favorable agreement to a rectangular wing wind-tunnel experiment. An advantage of this method is its ability to produce high-quality estimates of surface velocity, which is a valuable capability for interactive boundary-layer solvers.
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