Three-dimensional Cartesian parabolic equation model with higher-order cross-terms using operator splitting, rational filtering, and split-step Padé algorithm

Abstract

An approximate form of three-dimensional Cartesian split-step marching solution for the acoustic parabolic equation is derived in order to obtain the efficient algorithm for sound propagation in the three-dimensional ocean. The operator splitting method is used to split the full exponential operator into three exponential operators for depth, cross-range, and the combination of the two. The first two terms are implemented with the split-step Padé algorithm and the final term is implemented with the Taylor series expansion in depth and cross-range operator. In order to resolve the divergence of Taylor approximation out of the interval of convergence, the rational filter of rectangular type is applied to the depth and cross-range operator. The use of the filter improves the stability of the solution but requires extra numerical burdens. Numerical issues involving the accuracy, efficiency, and stability of the proposed model are discussed and illustrated in an ocean wedge environment.

Parallel optimization of underwater acoustic models: A survey

“…In 2019, Lee et al [42] developed a 3D parabolic equation model in a Cartesian coordinate system. The model contains the same higher-order cross terms as the 3D-PE models developed by Lin [43] and Sturm.…”

Three-Dimensional Modeling of Sound Field Holograms of a Moving Source in the Presence of Internal Waves Causing Horizontal Refraction

“…To achieve accurate and realistic simulations of the sound field structure, advanced numerical techniques and high-performance computer systems are often required. The numerical algorithms for sound field modeling in inhomogeneous waveguides can be divided into four main groups [24]: 3D Helmholtz equation (3DHE) models [25][26][27]; 3D parabolic equation (3DPE) models [28][29][30][31][32]; vertical modes and 2D modal parabolic equations (VMMPE) models [23,[33][34][35][36]; and 3D ray (3DR) models [37][38][39]. In the context of our study, we consider a low-frequency sound field (∆ f 1 = 100-120 Hz; ∆ f 2 = 300-320 Hz).…”