Ronald J. Epstein
Donald B. Bliss
Mech. Eng. and Mater. Sci., Duke Univ., Box 90300, Durham, NC 27708-90300
Analytical/numerical matching (ANM) is a hybrid scheme combining a low-resolution global numerical solution with a high-resolution local analytical solution to form a composite solution. ANM is applied to a harmonically vibrating flat plate in two dimensions to calculate the radiated acoustic field and the associated fluid loading. The problem utilizes overlapping smoothed doublets, and local corrections to calculate the doublet strength distribution along the plate. 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 doublets, and converges quickly. 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 an insensitivity to collocation point position. ANM provides high-resolution calculations from low-resolution numerics with analytical corrections, while avoiding the subtlety involving singular integral equations, and their numerical implementation. [Work supported by ONR.]