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A hybrid boundary element method for shallow water acoustic propagation over an irregular bottom. (English) Zbl 0957.76046
From the summary: We develop a hybrid numerical model combining a boundary element method (BEM) and eigenfunction expansions 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, we develop an adaptive integration technique and test it on 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. Finally, the model is used to study acoustic transmission over a rectangular bump in the bottom, as a function of frequency and bump geometry.

76M15 Boundary element methods applied to problems in fluid mechanics
76Q05 Hydro- and aero-acoustics
76B15 Water waves, gravity waves; dispersion and scattering, nonlinear interaction
Full Text: DOI
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