Abstract
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.
Highlights
In recent years, underwater acoustic technology has been widely used to measure ocean characteristics [1], detect underwater targets [2], and implement wireless underwater communication systems [3]
According to the different methods used in the test function, the spectral method discussed in this paper can be further divided into the Chebyshev–Galerkin spectral method and the Chebyshev collocation spectral method
Since the Chebyshev collocation spectral method has a wide range of applications and does not require strict boundary conditions, this method is applied to solve actual ocean acoustic calculation examples and analytical solutions are used to verify the correctness of the numerical results
Summary
Underwater acoustic technology has been widely used to measure ocean characteristics [1], detect underwater targets [2], and implement wireless underwater communication systems [3]. It is necessary to develop a direct solution to the two-dimensional Helmholtz equation of acoustic propagation without using simplified models. We first use the Chebyshev–Galerkin and Chebyshev collocation spectral methods to correctly solve the two-dimensional Helmholtz equation with Robin boundary conditions. It is feasible to use the collocation method to directly solve two-dimensional ocean acoustic propagation problems. We mainly study how to use the Chebyshev–Galerkin and Chebyshev collocation spectral methods to directly solve the two-dimensional Helmholtz equation with Robin boundary conditions. In the Chebyshev–Galerkin and Chebyshev collocation spectral methods, the two onedimensional trial functions are both Chebyshev polynomials or their linear combinations
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