Research PaperOpen Access

Applying the Chebyshev–Tau Spectral Method to Solve the Parabolic Equation Model of Wide-Angle Rational Approximation in Ocean Acoustics

Houwang Tu

https://orcid.org/0000-0002-1006-3932

College of Meteorology and Oceanography, National University of Defense Technology, Changsha 410073, P. R. China

E-mail Address: tuhouwang96@163.com

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Yongxian Wang

College of Meteorology and Oceanography, National University of Defense Technology, Changsha 410073, P. R. China

E-mail Address: yxwang@nudt.edu.cn

Corresponding author.

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Xian Ma

College of Meteorology and Oceanography, National University of Defense Technology, Changsha 410073, P. R. China

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, and

Xunjiang Zhu

College of Meteorology and Oceanography, National University of Defense Technology, Changsha 410073, P. R. China

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https://doi.org/10.1142/S2591728521500134Cited by:12 (Source: Crossref)

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.

Keywords:

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Vol. 30, No. 02

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History

Received 4 December 2020

Revised 19 May 2021

Accepted 28 May 2021

Published: 26 June 2021

Information

This is an Open Access article published by World Scientific Publishing Company. It is distributed under the terms of the Creative Commons Attribution 4.0 (CC BY) License which permits use, distribution and reproduction in any medium, provided the original work is properly cited.

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Applying the Chebyshev–Tau Spectral Method to Solve the Parabolic Equation Model of Wide-Angle Rational Approximation in Ocean Acoustics

Abstract

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