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Two Chebyshev Spectral Methods for Solving Normal Modes in Atmospheric Acoustics
The normal mode model is important in computational atmospheric acoustics. It is often used to compute the atmospheric acoustic field under a time-independent single-frequency sound source. Its solution consists of a set of discrete modes radiating into the upper atmosphere, usually related to the c...
Autores principales: | , , , , |
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Formato: | Online Artículo Texto |
Lenguaje: | English |
Publicado: |
MDPI
2021
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Materias: | |
Acceso en línea: | https://www.ncbi.nlm.nih.gov/pmc/articles/PMC8227614/ https://www.ncbi.nlm.nih.gov/pubmed/34199538 http://dx.doi.org/10.3390/e23060705 |
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author | Wang, Yongxian Tu, Houwang Liu, Wei Xiao, Wenbin Lan, Qiang |
author_facet | Wang, Yongxian Tu, Houwang Liu, Wei Xiao, Wenbin Lan, Qiang |
author_sort | Wang, Yongxian |
collection | PubMed |
description | The normal mode model is important in computational atmospheric acoustics. It is often used to compute the atmospheric acoustic field under a time-independent single-frequency sound source. Its solution consists of a set of discrete modes radiating into the upper atmosphere, usually related to the continuous spectrum. In this article, we present two spectral methods, the Chebyshev-Tau and Chebyshev-Collocation methods, to solve for the atmospheric acoustic normal modes, and corresponding programs are developed. The two spectral methods successfully transform the problem of searching for the modal wavenumbers in the complex plane into a simple dense matrix eigenvalue problem by projecting the governing equation onto a set of orthogonal bases, which can be easily solved through linear algebra methods. After the eigenvalues and eigenvectors are obtained, the horizontal wavenumbers and their corresponding modes can be obtained with simple processing. Numerical experiments were examined for both downwind and upwind conditions to verify the effectiveness of the methods. The running time data indicated that both spectral methods proposed in this article are faster than the Legendre-Galerkin spectral method proposed previously. |
format | Online Article Text |
id | pubmed-8227614 |
institution | National Center for Biotechnology Information |
language | English |
publishDate | 2021 |
publisher | MDPI |
record_format | MEDLINE/PubMed |
spelling | pubmed-82276142021-06-26 Two Chebyshev Spectral Methods for Solving Normal Modes in Atmospheric Acoustics Wang, Yongxian Tu, Houwang Liu, Wei Xiao, Wenbin Lan, Qiang Entropy (Basel) Article The normal mode model is important in computational atmospheric acoustics. It is often used to compute the atmospheric acoustic field under a time-independent single-frequency sound source. Its solution consists of a set of discrete modes radiating into the upper atmosphere, usually related to the continuous spectrum. In this article, we present two spectral methods, the Chebyshev-Tau and Chebyshev-Collocation methods, to solve for the atmospheric acoustic normal modes, and corresponding programs are developed. The two spectral methods successfully transform the problem of searching for the modal wavenumbers in the complex plane into a simple dense matrix eigenvalue problem by projecting the governing equation onto a set of orthogonal bases, which can be easily solved through linear algebra methods. After the eigenvalues and eigenvectors are obtained, the horizontal wavenumbers and their corresponding modes can be obtained with simple processing. Numerical experiments were examined for both downwind and upwind conditions to verify the effectiveness of the methods. The running time data indicated that both spectral methods proposed in this article are faster than the Legendre-Galerkin spectral method proposed previously. MDPI 2021-06-02 /pmc/articles/PMC8227614/ /pubmed/34199538 http://dx.doi.org/10.3390/e23060705 Text en © 2021 by the authors. https://creativecommons.org/licenses/by/4.0/Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/). |
spellingShingle | Article Wang, Yongxian Tu, Houwang Liu, Wei Xiao, Wenbin Lan, Qiang Two Chebyshev Spectral Methods for Solving Normal Modes in Atmospheric Acoustics |
title | Two Chebyshev Spectral Methods for Solving Normal Modes in Atmospheric Acoustics |
title_full | Two Chebyshev Spectral Methods for Solving Normal Modes in Atmospheric Acoustics |
title_fullStr | Two Chebyshev Spectral Methods for Solving Normal Modes in Atmospheric Acoustics |
title_full_unstemmed | Two Chebyshev Spectral Methods for Solving Normal Modes in Atmospheric Acoustics |
title_short | Two Chebyshev Spectral Methods for Solving Normal Modes in Atmospheric Acoustics |
title_sort | two chebyshev spectral methods for solving normal modes in atmospheric acoustics |
topic | Article |
url | https://www.ncbi.nlm.nih.gov/pmc/articles/PMC8227614/ https://www.ncbi.nlm.nih.gov/pubmed/34199538 http://dx.doi.org/10.3390/e23060705 |
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