Applying a Legendre collocation method based on domain decomposition to calculate underwater sound propagation in a horizontally stratified environment

Tu, Houwang; Wang, Yongxian; Liu, Qiang; Liu, Wei; Xiao, Wenbin; Ma, Shaoping

doi:10.1016/j.jsv.2021.116364

Cited by 18 publications

(10 citation statements)

References 19 publications

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“…Finally, in the third step of the algorithm, the eigenmodes of all segments must be transformed to the same vertical resolution. Thus, the Tau-type spectral method is used to solve for the eigenvalues and eigenmodes instead of the more convenient spectral collocation method 25 . The eigenmodes obtained by the spectral collocation method are the values at the collocation points, and the eigenmodes of J segments must be interpolated to the same vertical resolution.…”

Section: Discussionmentioning

confidence: 99%

“…In solving the range-independent normal modes, COUPLE employs the Galerkin method; however, finite difference method such as Kraken are traditionally used 18 . In recent years, many studies have begun to solve the acoustic propagation model by applying more accurate spectral methods [19][20][21][22][23][24][25] . In 1993, Dzieciuch 26 first used the Chebyshev-Tau spectral method to solve for the normal modes of the water column.…”

Section: Introductionmentioning

confidence: 99%

“…Numerical experiments show that the NM-CT program 28 based on the Chebyshev-Tau spectral method is faster than the rimLG program 27 based on Legendre-Galerkin spectral method and more accurate than the classic finite difference method 18 . Recently, Sabatini et al 29 and Tu et al 25,30 used Chebyshev collocation method and Legendre collocation method, respectively, to solve the problem of acoustic propagation in an ocean environment with any number of layers.…”

Section: Introductionmentioning

confidence: 99%

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An efficient numerical algorithm for solving range-dependent underwater acoustic waveguides based on a direct global matrix of coupled modes and the Chebyshev-Tau spectral method

Tu¹,

Wang²,

Chao³

et al. 2021

Preprint

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Sound propagation in a range-dependent ocean environment has long been a matter of widespread concern in ocean acoustics. Stepwise coupled modes is one of the main methods to solve range-dependent acoustic propagation problems. Underwater sound propagation satisfies a Helmholtz equation, the solution of which represents the core of computational ocean acoustics. Due to its high accuracy in solving differential equations, the spectral method has been introduced into computational ocean acoustics in recent years and has achieved remarkable results. However, the existing underwater acoustic propagation algorithms based on the spectral method can calculate only range-independent ocean acoustic waveguides, which excludes applications in more general range-dependent environments. In this paper, a complete and efficient algorithm is designed using an improved global matrix of coupled modes to solve the range dependence of the ocean environment and using the Chebyshev-Tau spectral method to precisely solve the eigenmodes in a stepped range-independent stair. Based on this algorithm, a complete and efficient numerical program is developed, and the numerical simulation results verify that this algorithm is extremely computationally fast and accurate for various range dependence and seabed environments.

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Section: Discussionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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An efficient numerical algorithm for solving range-dependent underwater acoustic waveguides based on a direct global matrix of coupled modes and the Chebyshev-Tau spectral method

Tu¹,

Wang²,

Chao³

et al. 2021

Preprint

Self Cite

View full text Add to dashboard Cite

show abstract

“…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].…”

Section: Introductionmentioning

confidence: 99%

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

Tu,

Wang,

Yang

et al. 2021

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High-precision numerical sound field is the basis of underwater target detection, positioning and communication. A line source in the plane is a common type of sound source in computational ocean acoustics, and the exciting waveguide in a range-dependent marine environment is often structurally complicated. However, traditional algorithms often assume that the waveguide has a simple seabed boundary, and the line source is located at a horizontal range of 0 m, which is an ideal and rare situation in the actual ocean. In this paper, a novel algorithm is designed that can solve for the sound field generated by a line source at any position in a range-dependent ocean environment. The proposed algorithm uses the classic stepwise approximation to address the range dependence

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“…Subsequently, Tu et al [11][12][13] 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 Chebyshev-Collocation method and proved that both of the spectral methods had high accuracy 14 . They also applied the spectral methods to the parabolic approximation of underwater acoustics 11,15,16 .…”

Section: Introductionmentioning

confidence: 99%

Two Chebyshev Spectral Methods for Solving Normal Modes in Atmospheric Acoustics

Houwang,

Yongxian,

Wenbin

et al. 2021

Preprint

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The normal mode model is important in computational atmospheric acoustics. It is often used to compute the atmospheric acoustic field under a harmonic point 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 were 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 obtaining the eigenvalues and eigenvectors, 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.

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Applying a Legendre collocation method based on domain decomposition to calculate underwater sound propagation in a horizontally stratified environment

Cited by 18 publications

References 19 publications

An efficient numerical algorithm for solving range-dependent underwater acoustic waveguides based on a direct global matrix of coupled modes and the Chebyshev-Tau spectral method

An efficient numerical algorithm for solving range-dependent underwater acoustic waveguides based on a direct global matrix of coupled modes and the Chebyshev-Tau spectral method

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

Two Chebyshev Spectral Methods for Solving Normal Modes in Atmospheric Acoustics

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