Applying the Chebyshev-Tau spectral method to solve the parabolic equation model of wide-angle rational approximation in ocean acoustics

TL;DR

This paper introduces a Chebyshev spectral method for solving the parabolic equation in ocean acoustics, demonstrating higher accuracy and efficiency over traditional finite difference methods in range-independent waveguides.

Contribution

The paper develops a Chebyshev spectral method-based discrete PE model for ocean acoustics, offering improved accuracy and computational speed over existing finite difference approaches.

Findings

Higher accuracy than RAM in simulations

Fewer grid points needed for the same precision

Faster computation after optimization

Abstract

Solving an acoustic wave equation using a parabolic approximation is a popular approach for many existing 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 wide-angle rational approximation, a discrete PE model using the Chebyshev spectral method (CSM) is derived, and the code is developed. This method is currently suitable only for range-independent waveguides. Taking three ideal fluid waveguides as examples, the correctness of using the CSM discrete PE model in solving the underwater acoustic propagation problem is verified. The test results show that compared with the RAM, the method proposed in this paper can achieve higher accuracy in computational underwater acoustics and requires fewer discrete grid points. After optimization, this method is more advantageous than the FDM in terms of speed. Thus, the CSM provides high-precision reference standards for benchmark examples of the range-independent PE model.