A novel approach to aerodynamic analysis using analytical/numerical matching
Analytical/Numerical Matching (ANM) is a hybrid scheme combining a low-resolution global numerical solution with a high-resolution local solution to form a composite solution. ANM is applied to lifting surfaces in steady potential flow to calculate the aerodynamic loading and associated circulation distribution. The solution methodology utilizes overlapping smoothed doublets, and local corrections to calculate the doublet strength distribution along the airfoil chord. A smoothing length scale is introduced that is larger than the smallest physical scale, and smaller than the largest physical scale. The global low-resolution solution is calculated numerically using smoothed doublet solutions to the linear potential equation, and converges quickly. Simultaneous local corrections are done with high-resolution local analytical solutions. The global numerical solution is asymptotically matched to the local analytical solutions via a matching solution. The matching solution cancels the global solution in the near-field, and cancels the local solution in the far-field. The method is very robust, offering insensitivity to control point location. No explicit wake geometry is assumed, therefore a fixed or free wake model can be used. ANM provides high resolution calculations from low resolution numerics with analytical corrections, while avoiding the subtlety involving singular integral equations, and their numerical implementation. The approach presented provides a novel alternative treatment to lifting surface aerodynamics.
