An examination of higher-order treatments of boundary conditions in split-step Fourier parabolic equation models
Smith, Kevin B.
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Parabolic equation models solved using the split-step Fourier (SSF) algorithm, such as the Monterey Miami Parabolic Equation model, are commonly used to predict underwater sound propagation in deep and shallow water environments. Previous studies have shown that the SSF algorithm is very accurate in shallow water when there is no density discontinuity between the water column and the sediment, but less effective in the presence of realistic density discontinuities due to phase errors that accumulate after a few kilometers. In this thesis, the standard density-smoothing approach and an alternative hybrid split-step/finite difference method are compared. The goal is to decrease the phase errors and increase the model’s long-range accuracy. Different depth meshes and range step sizes are implemented in the algorithm to find the optimum results for both approaches. It is shown that the density-smoothing method provides better results with small range step sizes, while the hybrid method is more effective using longer range step sizes. However, the smoothing approach provides a more stable convergence of results, whereas the hybrid method solution is more sensitive to change in computational grid sizes. A more detailed examination of the density smoothing approach suggests good accuracy for a few kilometers, while the hybrid method provides improved agreement with a benchmark solution at longer ranges.
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