A Spectral Method for Depth-Separated Solution of a Wavenumber Integration Model in Horizontally Stratified Fluid Acoustic Waveguides

The wavenumber integration model is considered to be the most accurate algorithm for arbitrary horizontally stratified media in computational ocean acoustics. In contrast to the normal mode approach, it considers not only the discrete wavenumber spectrum but also the continuous spectrum components, eliminating errors in the model approximation for horizontally stratified media. Traditionally, analytical and semianalytical methods have been used to solve the depth-separated wave equation in the wavenumber integration method, and numerical solutions have generally focused on the finite difference method and the finite element method. In this paper, an algorithm for solving the depth equation using the Chebyshev--Tau spectral method combined with a domain decomposition strategy is proposed, and a numerical program named WISpec is developed accordingly. The proposed algorithm can simulate not only the sound field excited by a point source but also the sound field excited by an infinite line source. The key idea of the algorithm is to first discretize the depth equations for each layer via the Chebyshev--Tau spectral method and then solve the equations for each layer simultaneously by incorporating boundary and interface conditions. Several representative numerical experiments are devised to test the accuracy and speed of WISpec. The high consistency of the results of different software programs running under the same configuration proves that the numerical algorithm proposed in this paper is accurate, reliable and numerically stable.