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

The parabolic approximation has been used extensively for underwater acoustic propagation and is attractive because it is computationally efficient. Widely used parabolic equation (PE) model programs such as the range-dependent acoustic model (RAM) are discretized by the finite difference method. Based on the idea of the Pad
 $$\acute{\text {e}}$$
 series expansion of the depth operator, a new discrete PE model using the Chebyshev collocation method (CCM) is derived, and the code (CCMPE) is developed. Taking the problems of four ideal fluid waveguides as experiments, the correctness of the discrete PE model using the CCM to solve a simple underwater acoustic propagation problem is verified. The test results show that the CCMPE developed in this article achieves higher accuracy in the calculation of underwater acoustic propagation in a simple marine environment and requires fewer discrete grid points than the finite difference discrete PE model. Furthermore, although the running time of the proposed method is longer than that of the finite difference discrete PE program (RAM), it is shorter than that of the Chebyshev–Tau spectral method.

Application of a Chebyshev Collocation Method to Solve a Parabolic Equation Model of Underwater Acoustic Propagation

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.

A Chebyshev-Tau spectral method for solving the parabolic equation model of wide-angle rational approximation in ocean acoustics.

The phenomenon of acoustic wave reflection off fluid–solid surfaces is the focus of this research. This research aims to measure the effect of material physical qualities on oblique incidence acoustic attenuation across a large frequency range. To construct the extensive comparison shown in the supporting documentation, reflection coefficient curves were generated by carefully adjusting the porousness and permeability of the poroelastic solid. The next stage in determining its acoustic response is to determine the pseudo-Brewster angle shift and the reflection coefficient minimum dip for the previously indicated attenuation permutations. This circumstance is made possible by modeling and studying the reflection and absorption of acoustic plane waves encountering half-space and two-layer surfaces. For this purpose, both viscous and thermal losses are taken into account. According to the research findings, the propagation medium has a significant impact on the form of the curve that represents the reflection coefficient, whereas the effects of permeability, porosity, and driving frequency are relatively less significant to the pseudo-Brewster angle and curve minima, respectively. This research additionally found that as permeability and porosity increase, the pseudo-Brewster angle shifts to the left (proportionally to porosity increase) until it reaches a limiting value of 73.4 degrees, and that the reflection coefficient curves for each level of porosity exhibit a greater angular dependence, with an overall decrease in magnitude at all incident angles. These findings are given within the framework of the investigation (in proportion to the increase in porosity). The study concluded that when permeability declined, the angular dependence of frequency-dependent attenuation reduced, resulting in iso-porous curves. The study also discovered that the matrix porosity largely affected the angular dependency of the viscous losses in the range of 1.4 × 10−14 m2 permeability.

/pdf/acoustic-wave-reflection-in-water-affects-underwater-1o51p4cz.pdf

Acoustic Wave Reflection in Water Affects Underwater Wireless Sensor Networks

/pdf/a-novel-algorithm-to-solve-for-an-underwater-line-source-14sagocs.pdf

A novel algorithm to solve for an underwater line source sound field based on coupled modes and a spectral method

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.

/pdf/a-chebyshev-spectral-method-for-normal-mode-and-parabolic-39h6vg5hyk.pdf

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

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 for solving 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, thereby excluding 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 employing 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 results of numerical simulations verify that this algorithm is extremely computationally fast and accurate for various range dependence and seabed environments.

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

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

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