Stephan T. Grilli and Torstein Pedersen and Peter Stepanishen
Associate Professor Graduate
student Professor
Department of Ocean Eng. Department
of Ocean Eng.
University of Rhode Island University
of Rhode Island
Narragansett, RI 02882, USA
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''.
Keywords :
Underwater acoustic, shallow water acoustic, wave propagation, boundary element method, hybrid-BEM.