In this paper, the Chebyshev spectral method is used to solve the normal mode and parabolic equation models of underwater acoustic propagation, and the results of the Chebyshev spectral method and the traditional finite difference method are compared for an ideal fluid waveguide with a constant sound velocity and an ideal fluid waveguide with a deep-sea Munk speed profile. The research shows that, compared with the finite difference method, the Chebyshev spectral method has the advantages of a high computational accuracy and short computational time in underwater acoustic propagation.

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.

The accuracy and efficiency of sound field calculations highly concern issues of hydroacoustics. Recently, one-dimensional spectral methods have shown high-precision characteristics when solving the sound field but can solve only simplified models of underwater acoustic propagation, thus their application range is small. Therefore, it is necessary to directly calculate the two-dimensional Helmholtz equation of ocean acoustic propagation. Here, we use the Chebyshev–Galerkin and Chebyshev collocation methods to solve the two-dimensional Helmholtz model equation. Then, the Chebyshev collocation method is used to model ocean acoustic propagation because, unlike the Galerkin method, the collocation method does not need stringent boundary conditions. Compared with the mature Kraken program, the Chebyshev collocation method exhibits a higher numerical accuracy. However, the shortcoming of the collocation method is that the computational efficiency cannot satisfy the requirements of real-time applications due to the large number of calculations. Then, we implemented the parallel code of the collocation method, which could effectively improve calculation effectiveness.

It is one of the most concerning problems in hydroacoustics to find a method that can calculate the acoustic propagation accurately and adapt to the variation of the seabed. Currently, the one-dimensional spectral method has been employed to address the simplified ocean acoustic propagation model successfully. However, due to the model's application limitations and approximation error, it poses challenges when attempting to solve real-world ocean acoustic fields. Hence, there is a crucial need to develop a direct solution method for the two-dimensional Helmholtz equation of ocean acoustic propagation, without relying on a simplified model. In previous work, we achieved successful solutions for the two-dimensional Helmholtz equation within a rectangular domain, utilizing a collocation-type spectral method. Taking into account the fluctuations in the actual seabed, we introduce a Chebyshev collocation spectral method to directly tackle the two-dimensional ocean acoustic propagation problem, which could solve the case of a seabed with linear variation, sound velocity variation and inhomogeneous medium situation. After comparative verification, the calculation result of the two-dimensional spectral method is more accurate than traditional mature models such as Kraken and COUPLE. By eliminating model constraints and enlarging the solution range, this spectral method holds immense potential in real marine environments.

Accurate calculations of ocean acoustic propagation are of significant importance in various aspects such as marine environmental monitoring, oceanic communication, and navigation. Various mature simplified models have been developed, such as the normal mode model, parabolic approximation model, and wavenumber integration model. The above-mentioned models and algorithms all have limitations, namely, “applicable domain,” which restrict their range of application. Instead of simplifying model, the algorithm described in this article aims at solving the Helmholtz equation, which governs ocean acoustic propagation. It solves the ocean acoustic propagation without being constrained by model application conditions and has a wide range of applications, which is a versatile method for solving acoustic propagation. The algorithm utilizes Chebyshev tau matrix method to directly solve the two-dimensional acoustic Helmholtz equation, which could solve the situation of uneven media within irregular domain, addressing the issue of traditional spectral method being unsuitable for non-rectangular domain. Compared with the mature programs, the new spectral method offers higher computational accuracy and is capable of calculating acoustic propagation in more complex ocean environments.