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.

Sound waves can be used to carry out underwater activities. Rapidly and accurately simulating sound propagation is the basis for underwater detection. The wide-angle parabolic model has a good computational speed and accuracy and is currently the main numerical model for mid- and low-frequency sound propagation. The classical wide-angle parabolic equation model is discretized by the finite difference method and a low-order difference scheme is generally adopted. In this paper, a wide-angle parabolic equation model based on a spectral method is proposed. The depth operators of each layer are discretized via the Chebyshev spectral method and then assembled into a global matrix for the forward step. Lateral inhomogeneity is addressed by updating the global depth matrix while stepping forward. In the proposed spectral algorithm, both soft and hard seabeds can be accurately simulated by imposing boundary conditions, and the perfectly matched layer technique is used to truncate the unbounded acoustic half-space. Several representative numerical experiments prove the accuracy and efficiency of the proposed algorithm. However, the spectral method requires that the thickness of the layers does not change during the forward step. Thus, the current spectral algorithm cannot simulate waveguides with terrain undulation, which is its main limitation.