A FINITE DIFFERENCE SOLUTION TO THE HELMHOLTZ EQUATION IN A RADIALLY SYMMETRIC WAVEGUIDE: APPLICATION TO NEAR-SOURCE SCATTERING IN OCEAN ACOUSTICS

摘要

A finite difference (FD) method is developed and analyzed for the Helmholtz equation in a radially symmetric waveguide. The resulting algorithm can be used to solve for sound intensities in complex models that may include high material contrasts and arbitrary bathymetry. An analysis of the effect of grid discretization on the results indicates that numerical dispersion is significant within one-third of a wavelength from a point source and decreases beyond that. Numerical results are presented and compared to wide-angle parabolic equation (PE) solutions and analytic solutions, where available. Comparison with analytic results indicates that the FD method accurately solves for the acoustic wave field at all propagation angles and is more accurate than the PE method near the source. Results are also shown for models in which mode coupling occurs near the source.