A three-dimensional parabolic equation model of sound propagation using higher-order operator splitting and Padé approximants

Abstract

An alternating direction implicit (ADI) three-dimensional fluid parabolic equation solution method with enhanced accuracy is presented. The method uses a square-root Helmholtz operator splitting algorithm that retains cross-multiplied operator terms that have been previously neglected. With these higher-order cross terms, the valid angular range of the parabolic equation solution is improved. The method is tested for accuracy against an image solution in an idealized wedge problem. Computational efficiency improvements resulting from the ADI discretization are also discussed.

Time-evolving acoustic propagation modeling in a complex ocean environment

“…The obvious course of action is to improve the quality of the modeling and of the inputs that it requires. The shortcomings of the acoustic model shown here are addressed, for instance through the development of 3D acoustic propagation models [38]. Another necessary measure is to accompany predictions with a measure of uncertainty.…”

Mode Gaussian beam tracing

“…Moreover it is necessary to consider only the exited modes which present explicitly in the final solution. On the other hand, in the parabolic equation [8,9] we should consider the large number of modes with their interactions. Thus, many effects previously described in the terms of the mode interaction can be explained in the terms of the horizontal refraction.…”

Three-Dimensional Shallow Water Acoustics

“…In the split-step Fourier PE, they are the free-space propagator and the medium phase speed anomalies, respectively [5]. In the split-step Padé PE, they are the derivations in the horizontal and vertical directions [6].…”

“…A 3-D normal mode method has been used to study canonical environmental models of shelfbreak front systems [1] and nonlinear internal wave ducts [2][3]. 3-D parabolic-equation (PE) wave propagation models with improved split-step marching algorithms [4][5][6] are used to study sound propagation in realistic environments. When the acoustic mode coupling can be neglected, a vertical-mode horizontal-PE model is used.…”