A Chebyshev tau matrix method to directly solve two-dimensional ocean acoustic propagation in undulating seabed environment

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.