Applying a Legendre collocation method based on domain decomposition to calculate underwater sound propagation in a horizontally stratified environment. (27th October 2021) - Tu, Houwang
Abstract: The propagation of sound waves in a horizontally stratified environment, a classic problem in ocean acoustics, has traditionally been calculated using normal modes. Most programs based on the normal mode model are discretized using the finite difference method (FDM). In this paper, a Legendre collocation method (LCM) based on domain decomposition is proposed to solve this problem. A set of collocation points cannot penetrate multiple layers of media, thus necessitating domain decomposition and the use of multiple sets of collocation points. The solution process of this method proceeds entirely in physical space, requiring that the original differential equation be strictly established at the collocation points; thus, a dense matrix eigenvalue system is formed, from which the solution for the horizontal wavenumbers and modes can be directly obtained. Numerical experiments are presented to demonstrate the validity and applicability of this method. A comparison with other methods shows that the LCM proposed in this article is more accurate than the FDM and offers approximately the same accuracy as, but a faster calculation speed than, other types of spectral methods. Highlights: This paper proposes a new method to calculate acoustic propagation in horizontally stratified marine environment. The accuracy of the new method is greater than that of the classical finite difference method. The new method is far faster than the Legendre-Galerkin and Chebyshev-Tau spectral methods.