Residual potential method in spherical coordinates and related approximations

Abstract

The Residual Potential Method, introduced by Geers [ l ] , appears to be a very promising technique in the solution of sol id-f luid interaction problems. The theoretical development of the method in cylindrical coordinates was presented in [1,2]. In [3], Geers presents some numerical results obtained using the Residual Potential Method in spherical coordinates; however, the theoretical treatment is not provided. The purpose of the present work is to express the classical spherical wave equation in terms of a residual potential and to discuss the accuracy of the various forms of the related acoustic approximations.