A hybrid boundary element method for shallow water acoustic propagation over an irregular bottom

Abstract

A hybrid numerical model combining a boundary element method (BEM) and eigenfunction expansions is developed to solve acoustic wave propagation in shallow water. Waves are assumed harmonic and, therefore, the governing equation reduces to a Helmholtz equation. Accurate numerical integration techniques are implemented in the BEM, for calculating singular and quasi-singular integrals. For the latter, an adaptive integration technique is developed and tested for computational domains with very small aspect ratios, representative of shallow water environments. The model is validated by comparing the numerical solution to analytic solutions for problems with simple boundary geometries (e.g. rectangular, step, and sloped domains). Results indicate good agreement between the two solutions. Effects of node resolution, adaptive integrations, and number of modes in radiated fields, on the accuracy of the solution, are assessed. Finally, the model is used to study acoustic transmission over a rectangular bump in the bottom, as a function of frequency and bump geometry. Expected results are obtained below the first cut-off frequency over the bump, i.e. the transmission of energy beyond the bump through evanescent modes. A similar effect is commonly noted in layered media and is known as ‘tunneling’.