Comparison of two-dimensional axial-symmetric and longitudinally invariant methods for three-dimensional shallow water acoustic propagation using finite element methods

Abstract

In shallow water acoustic propagation, performing a fully three-dimensional finite element model is currently unfeasible due to difficulty in implementation and limits in computational power. Therefore, alternative representations of the 3D acoustic field are sought. Two promising methods to represent the 3D field are the longitudinally invariant (LI) method, and a 2D axial-symmetric reduction of the 3D Helmholtz equation. When a spherical source is used, azimuthal symmetry of the acoustic propagation is assumed, and these two methods can be compared in 2D planes of the 3D field. Because the LI method takes more computational time than the axial-symmetric method, the accuracy of the pressure field are compared to see if the axial-symmetric method can be used in place of the LI method. First, the two methods are compared for a flat ocean surface with stratified media. Then, a wedge-shaped ocean surface is considered, and the two methods are compared with 2D PE solutions. These comparisons will show if the axial-symmetric method produces similar results to the LI method, and if so, under which geometrical and physical situations the axial-symmetric method can be used in place of the LI method. [Work sponsored by the Office of Naval Research, Ocean Acoustics.]