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

The article focuses on a novel algorithm using the Chebyshev tau matrix spectral method to directly solve the two-dimensional Helmholtz equation governing ocean acoustic propagation in irregular domains with uneven media. Unlike traditional simplified models—such as normal mode, parabolic equation, and wavenumber integration models—which have limited applicability and introduce approximation errors, this spectral method offers a universal, high-precision solution without model simplifications. Numerical examples demonstrate that the spectral method achieves significantly higher accuracy than mature finite-difference-based programs like Kraken, RAM, and COUPLE, effectively handling complex ocean environments including variable sound speed, fluctuating seabeds, and non-rectangular domains. While the method shows fast convergence and meshless computation advantages, challenges remain in computational efficiency for large systems and in managing boundary condition effects near sound shadow regions, which are identified as areas for future research.