An efficient numerical algorithm for solving range-dependent underwater acoustic waveguides based on a direct global matrix of coupled modes and the Chebyshev-Tau spectral method

Abstract

Sound propagation in a range-dependent ocean environment has long been a matter of widespread concern in ocean acoustics. Stepwise coupled modes is one of the main methods to solve range-dependent acoustic propagation problems. Underwater sound propagation satisfies a Helmholtz equation, the solution of which represents the core of computational ocean acoustics. Due to its high accuracy in solving differential equations, the spectral method has been introduced into computational ocean acoustics in recent years and has achieved remarkable results. However, the existing underwater acoustic propagation algorithms based on the spectral method can calculate only range-independent ocean acoustic waveguides, which excludes applications in more general range-dependent environments. In this paper, a complete and efficient algorithm is designed using an improved global matrix of coupled modes to solve the range dependence of the ocean environment and using the Chebyshev-Tau spectral method to precisely solve the eigenmodes in a stepped range-independent stair. Based on this algorithm, a complete and efficient numerical program is developed, and the numerical simulation results verify that this algorithm is extremely computationally fast and accurate for various range dependence and seabed environments.

A Spectral Method for Depth-Separated Solution of a Wavenumber Integration Model in Horizontally Stratified Fluid Acoustic Waveguides

“…In mathematical monographs, the above equation is generally called the weak form [18] of Eq. (30). Taking into account the orthogonality of the Chebyshev polynomial and Eq.…”

“…Spectral methods have high accuracy and fast convergence speed [14][15][16][17][18][19][20] and have been rapidly developed in acoustics [21,22], especially computational ocean acoustics. In recent years, new algorithms of normal modes [23][24][25][26][27][28][29], coupled modes [30][31][32] and parabolic equation models [33][34][35] based on spectral methods have been successively proposed. In this paper, a Chebyshev-Tau spectral method is used to numerically solve the depth-separated wave equation.…”

Application of a Spectral Method to Simulate Quasi-Three-Dimensional Underwater Acoustic Fields

“…Our model adopts an absorbing layer to simulate the acoustic half-space, which overcomes the shortcomings of Sabatini's algorithm, namely, matrices that are twice as large and a slow computational speed. Additionally, we conducted research on solving parabolic equation models with the spectral method [19][20][21] and subsequently proposed a spectral method-based algorithm for solving acoustic propagation in a two-dimensional, range-dependent marine environment [22,23].…”

A Novel Algorithm to Solve for an Underwater Line Source Sound Field Based on Coupled Modes and a Spectral Method

“…As a high-precision method for solving differential equations, the spectral method was introduced into computational ocean acoustics at the end of the twentieth century [17][18][19]. Using this method, our team has performed a series of studies to solve underwater acoustic propagation models in recent years [20][21][22][23][24][25][26]. In particular, we developed a normal mode solver named NM-CT based on the Chebyshev-Tau spectral method and provided the code in the opensource Ocean Acoustics Library (OALIB) [27].…”