Spectral methods are a new and niche numerical discretization method with the main characteristic of high accuracy. Spectral methods have been applied in many fields of engineering numerical simulation. Since their introduction into ocean acoustics in 1993, spectral methods have made significant progress in computational ocean acoustics. This article systematically introduces the basic principles of spectral methods, their applicable conditions, and their applications and developments in the normal mode model, the wavenumber integration model, the parabolic equation model, and acoustic Helmholtz equation simulations. At the same time, this article points out the shortcomings of the current application of spectral methods in computational ocean acoustics and potential research directions in the future. The aim is to provide a comprehensive research foundation for subsequent researchers and to promote the application of spectral methods in computational ocean acoustics to go further and deeper.

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