A Spectral Method for Two-Dimensional Ocean Acoustic Propagation

Abstract

The accurate calculation of the sound field is one of the most concerning issues in hydroacoustics. The one-dimensional spectral method has been used to correctly solve simplified underwater acoustic propagation models, but it is difficult to solve actual ocean acoustic fields using this model due to its application conditions and approximation error. Therefore, it is necessary to develop a direct solution method for the two-dimensional Helmholtz equation of ocean acoustic propagation without using simplified models. Here, two commonly used spectral methods, Chebyshev–Galerkin and Chebyshev–collocation, are used to correctly solve the two-dimensional Helmholtz model equation. Since Chebyshev–collocation does not require harsh boundary conditions for the equation, it is then used to solve ocean acoustic propagation. The numerical calculation results are compared with analytical solutions to verify the correctness of the method. Compared with the mature Kraken program, the Chebyshev–collocation method exhibits higher numerical calculation accuracy. Therefore, the Chebyshev–collocation method can be used to directly solve the representative two-dimensional ocean acoustic propagation equation. Because there are no model constraints, the Chebyshev–collocation method has a wide range of applications and provides results with high accuracy, which is of great significance in the calculation of realistic ocean sound fields.

Dynamical Analysis of Two-Dimensional Fractional-Order-in-Time Biological Population Model Using Chebyshev Spectral Method

“…In this section, we present some basic definitions related to fractional calculus theory and orthogonal polynomials that are useful in the error analysis of our proposed numerical scheme [44][45][46][47]. Definition 1.…”

A Lattice-adaptive Model for Solving Acoustic Wave Equations Based on Lattice Boltzmann Method

“…The investigation of wave propagation in fluid media by studying wave problems has been pursued by two different methods. The first method involves the direct solution of the fluid conservation equations, namely the Navier-Stokes equations (7)(8)(9)(10)(11). The second method involves the solution of the simplified and combined fluid conservation equations, commonly referred to as wave equation-based models (12)(13)(14)(15)(16).…”

A Vector Wavenumber Integration Model of Underwater Acoustic Propagation Based on the Matched Interface and Boundary Method

“…Ocean acoustic waves propagate over long distances because their energy attenuates less in water than does that of electromagnetic waves; consequently, acoustic waves have been widely used in target detection, environmental monitoring, and underwater communication [1]. Underwater acoustic wave propagation excited by a time harmonic source can be described by the Helmholtz equation in the frequency domain, which can be solved using the wavenumber integration technique [2,3], the fast field program (FFP) [4][5][6], normal modes [7], ray theory [8], the parabolic equation [9], the finite difference method (FDM) [10], and the spectral method [11]. As these models for predicting the scalar sound level have reached a high level of development, our interest herein is in developing a vector model to accurately predict the particle velocity.…”

“…The objective of this study was to obtain the most accurate vector acoustic model possible that can be used to provide benchmark solutions in range-independent environments for verifying other numerical acoustic models, such as FDM models [10] and spectral method models [11]. However, although the normal mode method, parabolic equation, and FFP mentioned above have the advantages of a small computational load and good numerical stability, they have difficulty effectively satisfying the required accuracy due to approximation errors.…”