A Chebyshev-Tau spectral method for normal modes of underwater sound propagation with a layered marine environment

Abstract: The normal mode model is one of the most popular approaches for solving underwater sound propagation problems. Among other methods, the finite difference method is widely used in classic normal mode programs. In many recent studies, the spectral method has been used for discretization. It is generally more accurate than the finite difference method. However, the spectral method requires that the variables to be solved are continuous in space, and the traditional spectral method is powerless for a layered marine environment. A Chebyshev-Tau spectral method based on domain decomposition is applied to the construction of underwater acoustic normal modes in this paper. In this method, the differential equation is projected onto spectral space from the original physical space with the help of an orthogonal basis of Chebyshev polynomials. A complex matrix eigenvalue / eigenvector problem is thus formed, from which the solution of horizontal wavenumbers and modal functions can be solved. The validity of the acoustic field calculation is tested in comparison with classic programs. The results of analysis and tests show that compared with the classic finite difference method, the proposed Chebyshev-Tau spectral method has the advantage of high computational accuracy. In addition, in terms of running time, our method is faster than the Legendre-Galerkin spectral method.