A spectral method for the depth-separated solution of a wavenumber integration model for horizontally stratified fluid acoustic waveguides

The wavenumber integration model is the most precise approach for assessing arbitrary horizontally stratified media within the sphere of computational ocean acoustics. Unlike the normal-mode approach, it considers not only discrete spectra but also continuous spectral components, resulting in fewer model approximation errors for horizontally stratified media. Traditionally, the depth-separated wave equation in the wavenumber integration model has been solved using analytical and semianalytical methods, and numerical solutions have been primarily based on the finite difference and finite element methods. This paper proposes an algorithm for solving the depth equation via the Chebyshev-Tau spectral method, combined with a domain decomposition strategy, resulting in the development of a numerical program named WISpec. The algorithm can simulate the sound field excitation not only from a point source but also from an infinite line source. To that end, the depth equations for each layer are first discretized through the Chebyshev-Tau spectral method and subsequently solved simultaneously by incorporating boundary and interface conditions. Representative numerical experiments are presented to validate the accuracy and speed of WISpec. The high degree of consistency of results obtained from different software tools running the same configuration provides ample evidence that the numerical algorithm described in this paper is accurate, reliable, and numerically stable.

Automated summary

The wavenumber integration model is proposed as a precise method for assessing horizontally stratified media in computational ocean acoustics. This paper presents an algorithm, combining the Chebyshev-Tau spectral method and domain decomposition, for solving the depth equation and develops a numerical program named WISpec. The accuracy and speed of WISpec are validated through representative numerical experiments.