A Chebyshev–Tau spectral method for coupled modes of underwater sound propagation in range-dependent ocean environments

Abstract

A coupled-mode model is a classic approach for solving range-dependent sound propagations and is often used to provide benchmark solutions in comparison with other numerical models because of its high accuracy. Existing coupled-mode programs have disadvantages such as high computational cost, weak adaptability to complex ocean environments, and numerical instability. In this paper, a new algorithm that uses an improved range normalization of a “stair-step” and global matrix approach to address range dependence in ocean environments is designed. This algorithm uses the Chebyshev–Tau spectral method to solve the eigenpairs in the range-independent segments. The Chebyshev–Tau spectral method can converge rapidly, and the rate of convergence depends on the smoothness of the sound speed and density profiles. The main steps of the algorithm are parallelized, so parallel computing technologies are also applied for further acceleration. Based on this algorithm, an efficient program is implemented, and numerical simulations verify that this algorithm is reliable, accurate, and capable. Compared with the existing coupled-mode programs, the newly developed program is more stable and efficient with comparable accuracy and can simulate waveguides in more complex and realistic ocean environments.