A Chebyshev Spectral Method for Normal Mode and Parabolic Equation Models in Underwater Acoustics

Abstract

In this paper, the Chebyshev spectral method is used to solve the normal mode and parabolic equation models of underwater acoustic propagation, and the results of the Chebyshev spectral method and the traditional finite difference method are compared for an ideal fluid waveguide with a constant sound velocity and an ideal fluid waveguide with a deep-sea Munk speed profile. The research shows that, compared with the finite difference method, the Chebyshev spectral method has the advantages of a high computational accuracy and short computational time in underwater acoustic propagation.

A Coupling Graphic Pipeline with Normal Mode Model for Rapid Calculation of Underwater Acoustic Field

“…where |p 0 (r)| � 1/(4πr). e first step of color mapping is to calculate TL by equation (7). en, TL is mapped to the brightness (B) in HSB color space.…”

“…However, when the resolution of the underwater sound field image is high, calculating sound field may take up a lot of computing resources. In [7], the computer times of two different numerical solutions for normal mode theory are tested using a one-thread CPU on Tianhe-2 supercomputer, and for both numerical solutions, the times to calculate sound field image are much longer than the times to calculate the modes. For operation-oriented applications, the acceleration in calculating sound field image is necessary.…”

Two Chebyshev Spectral Methods for Solving Normal Modes in Atmospheric Acoustics

“…In 2016, Evans [12] used the Legendre-Galerkin spectral method to develop a sound propagation calculation program in a layered ocean environment. Subsequently, Tu et al [13][14][15] used the Chebyshev-Tau spectral method to develop a program for calculating sound propagation in single-layer and layered ocean environments. They subsequently solved for the normal modes in underwater acoustics using the Legendre-Collocation method and proved that both of the spectral methods had high accuracy [16].…”

“…They subsequently solved for the normal modes in underwater acoustics using the Legendre-Collocation method and proved that both of the spectral methods had high accuracy [16]. They also applied the spectral methods to the parabolic approximation of underwater acoustics [13,17,18]. The results of these studies indicated that it is feasible to apply spectral methods for the calculation of underwater acoustics, and in many cases, it has higher accuracy than the finite difference method.…”

A Novel Algorithm to Solve for an Underwater Line Source Sound Field Based on Coupled Modes and a Spectral Method

“…As a high-precision method for solving differential equations, the spectral method was introduced into computational ocean acoustics at the end of the twentieth century [17][18][19]. Using this method, our team has performed a series of studies to solve underwater acoustic propagation models in recent years [20][21][22][23][24][25][26]. In particular, we developed a normal mode solver named NM-CT based on the Chebyshev-Tau spectral method and provided the code in the opensource Ocean Acoustics Library (OALIB) [27].…”