Abstract
The accurate calculation of the sound field is one of the most concerning issues in hydroacoustics. The one-dimensional spectral method has been used to correctly solve simplified underwater acoustic propagation models, but it is difficult to solve actual ocean acoustic fields using this model due to its application conditions and approximation error. Therefore, it is necessary to develop a direct solution method for the two-dimensional Helmholtz equation of ocean acoustic propagation without using simplified models. Here, two commonly used spectral methods, Chebyshev–Galerkin and Chebyshev–collocation, are used to correctly solve the two-dimensional Helmholtz model equation. Since Chebyshev–collocation does not require harsh boundary conditions for the equation, it is then used to solve ocean acoustic propagation. The numerical calculation results are compared with analytical solutions to verify the correctness of the method. Compared with the mature Kraken program, the Chebyshev–collocation method exhibits higher numerical calculation accuracy. Therefore, the Chebyshev–collocation method can be used to directly solve the representative two-dimensional ocean acoustic propagation equation. Because there are no model constraints, the Chebyshev–collocation method has a wide range of applications and provides results with high accuracy, which is of great significance in the calculation of realistic ocean sound fields.
Highlights
Because the finite difference method has difficulty dealing with the Helmholtz equation with complex boundary conditions, it is commonly used to deal with the simplified partial differential equation of the Helmholtz equation for ocean acoustic propagation
Since the Chebyshev–collocation spectral method has a wide range of applications and does not require strict boundary conditions as Galerkin method, it is applied to solve actual ocean acoustic calculation examples, and analytical solutions are used to verify the correctness of the numerical results
This paper uses the Chebyshev–Galerkin and Chebyshev–collocation spectral methods to directly solve two-dimensional Helmholtz model equations and uses an analytical solution to verify the correctness of the two methods
Summary
Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations. Because the finite difference method has difficulty dealing with the Helmholtz equation with complex boundary conditions, it is commonly used to deal with the simplified partial differential equation of the Helmholtz equation for ocean acoustic propagation. The Chebyshev–Galerkin and Chebyshev–collocation spectral methods are used to directly solve the two-dimensional Helmholtz equation with Robin boundary conditions, and the results are compared with those of the corresponding analytical solutions. In consideration of the complicated boundary conditions of the actual marine environment, the Chebyshev–collocation spectral method is used to solve the Helmholtz equation of twodimensional ocean acoustic propagation.
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