Aeroacoustic boundary element method using analytical/numerical matching

A unified aeroacoustic boundary element theory has been formulated using analytical/numerical matching (ANM). ANM is a hybrid scheme combining a low-resolution global numerical solution with high-resolution local solutions to form a composite solution. ANM is applied to problems in unsteady aerodynamics and aeroacoustics. This includes both two and three dimensions for lifting surfaces in unsteady, compressible, irrotational flow to calculate the unsteady aerodynamic loading and the associated acoustic field. The solution procedure utilizes overlapping smoothed doublets and local corrections to calculate the doublet strength distribution on the surface of the boundary in question. In ANM, a smoothing length scale is introduced that is larger than the length scale of numerical discretization and smaller than the largest physical scale. The global low-resolution solution is calculated numerically using smoothed doublet solutions to the convective wave equation, and it converges quickly. Local corrections are done with high-resolution analytical solution. 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 for field. The ANM composite solution gives both the surface pressure distribution and the radiated acoustic field. The method is very robust, offering insensitively to control point location. No explicit wake geometry is asssumed; 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 singlular integral equations, and their numerical implementation.