A Chebyshev-Tau spectral method for solving the parabolic equation model of wide-angle rational approximation in ocean acoustics

Solving an acoustic wave equation using a parabolic approximation is a popular approach for many available ocean acoustic models. Commonly used parabolic equation (PE) model programs, such as the range-dependent acoustic model (RAM), are discretized by the finite difference method (FDM). Considering the idea and theory of the "split-step" parabolic approximation, a discrete PE model using the Chebyshev spectral method (CSM) is derived, and the code is developed. We use the problems of two ideal fluid waveguides as examples, i.e., one with a constant sound speed in shallow water and one with a Munk sound speed profile in the deep ocean. The correctness of the discrete PE model using the CSM to solve a simple underwater acoustic propagation problem is verified. The test results show that compared with the finite difference discrete PE model, the proposed method in this paper has a higher accuracy in the calculation of underwater acoustic propagation in a simple marine environment and requires fewer discrete grid points. However, the proposed method has a longer running time than the finite difference discrete PE program. Thus, it is suitable to provide high-precision reference standards for the benchmark examples of the PE model.