A Chebyshev-Tau spectral method for normal modes of underwater sound propagation with a layered marine environment

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

doi:10.1016/j.jsv.2020.115784

Cited by 41 publications

(30 citation statements)

References 20 publications

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“…In the two spectral methods developed in this article, the basis functions φ k (x) are both Chebyshev polynomials T k (x), and the difference is the selection of weight functions. The Chebyshev polynomial basis functions are provided in [14,[20][21][22].…”

Section: Discretized Atmospheric Normal Modes By Two Spectral Methodsmentioning

confidence: 99%

“…This is why the Collocation method is considered to be a special spectral method, sometimes called the pseudospectral method [21]. In the Chebyshev-Collocation method, we also take the discrete points of the Chebyshev-Gauss-Lobatto nodes in Equation (14). In this case, the only difficulty is the discretization of operator L. The conclusions used in the following text are directly given here as in the introduction of the Chebyshev-Tau spectral method.…”

Section: Discretized Atmospheric Normal Modes By Chebyshev-collocation Spectral Methodsmentioning

confidence: 99%

“…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].…”

Section: Introductionmentioning

confidence: 99%

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Two Chebyshev Spectral Methods for Solving Normal Modes in Atmospheric Acoustics

Wang

Xiao

et al. 2021

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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 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.

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Section: Discretized Atmospheric Normal Modes By Two Spectral Methodsmentioning

confidence: 99%

Section: Discretized Atmospheric Normal Modes By Chebyshev-collocation Spectral Methodsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Two Chebyshev Spectral Methods for Solving Normal Modes in Atmospheric Acoustics

Wang

Xiao

et al. 2021

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“…Although the propagation of acoustic waves in the ocean is affected by both seawater and the ocean surface, acoustic waves of a fixed frequency can still be obtained after adding boundary conditions to constrain the elliptic partial differential Helmholtz equation [ 4 ]. Recently, our research group used the one-dimensional spectral method to correctly solve the normal modes in underwater sound propagation [ 5 ] and atmospheric acoustics [ 6 ], demonstrating that the spectral method has the advantages of fast convergence and high accuracy when solving the sound field. However, there are still some problems in this calculation process.…”

Section: Introductionmentioning

confidence: 99%

A High-Efficiency Spectral Method for Two-Dimensional Ocean Acoustic Propagation Calculations

Wang

Zhu

et al. 2021

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The accuracy and efficiency of sound field calculations highly concern issues of hydroacoustics. Recently, one-dimensional spectral methods have shown high-precision characteristics when solving the sound field but can solve only simplified models of underwater acoustic propagation, thus their application range is small. Therefore, it is necessary to directly calculate the two-dimensional Helmholtz equation of ocean acoustic propagation. Here, we use the Chebyshev–Galerkin and Chebyshev collocation methods to solve the two-dimensional Helmholtz model equation. Then, the Chebyshev collocation method is used to model ocean acoustic propagation because, unlike the Galerkin method, the collocation method does not need stringent boundary conditions. Compared with the mature Kraken program, the Chebyshev collocation method exhibits a higher numerical accuracy. However, the shortcoming of the collocation method is that the computational efficiency cannot satisfy the requirements of real-time applications due to the large number of calculations. Then, we implemented the parallel code of the collocation method, which could effectively improve calculation effectiveness.

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“…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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A Chebyshev-Tau spectral method for normal modes of underwater sound propagation with a layered marine environment

Cited by 41 publications

References 20 publications

Two Chebyshev Spectral Methods for Solving Normal Modes in Atmospheric Acoustics

Two Chebyshev Spectral Methods for Solving Normal Modes in Atmospheric Acoustics

A High-Efficiency Spectral Method for Two-Dimensional Ocean Acoustic Propagation Calculations

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

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