Application of Matched Expansion Methods to Problems in Acoustics

摘要

This report describes how the method of Matched Asymptotic Expansions (MAE) can be used safely and systematically (1) to indicate the appropriate from taken by the inner (near field) and outer (wave field) series and (2) to determine all unknown functions and constants appearing in both series by matching the series according to a clearcut rule. These points are illustrated by detailed study of several very simple problems in low-frequency acoustic scattering problems which serve to demonstrate that physical arguments are unreliable in these problems and that they are no substitute for the unambiguous matching rule. Two-dimensional scattering problems are used to introduce logarithmic gauge functions; it is shown that the matching rule can easily accommodate these functions and moreover, that insistence upon satisfaction of the matching rule can in some cases be used to greatly improve the rapidly of convergence of series involving logarithmic functions. The report emphasizes the very widespread applicability of the MAE method to problem in classical and modern, linear and nonlinear acoustics and related fields.