Three-dimensional boundary fitted parabolic-equation model of underwater sound propagation

A three-dimensional (3-D) parabolic-equation (PE) method utilizing a higher-order split-step Padé algorithm and a boundary fitted grid has been developed to accurately solve 3-D underwater sound propagation problems with non-planar or tilted boundaries. At each PE marching step, the split-step Padé algorithm enables the method of alternating directions to implement the square-root Helmholtz operator by carrying out its one-dimensional (1-D) derivative components alternately, and it also allows a straightforward application of the 1-D non-uniform Galerkin method to discretize the solution mesh. The advantage of the boundary fitted grid to improve PE solution accuracy is most profound in the case of fitting to a pressure release surface as its boundary condition is a scalar and has no direction. This method can also be applied to a sloping interface by rotating the grid to align with the interface. Numerical problems of semi-circular waveguide and tilted wedge were solved using this boundary fitted PE method, and benchmark reference solutions were used to examine and confirm the accuracy of the PE solutions. Future applications include modeling 3-D acoustic scattering from a rough sea surface and 3-D sound propagation in beach environments.