Underwater sound field numerical simulation method and system based on Chebyshev polynomial spectrum and medium

Abstract

The invention discloses an underwater sound field numerical simulation method and system based on a Chebyshev polynomial spectrum and a medium. The method comprises the following steps: establishing asimplified control equation of an acoustic propagation Helmholtz equation under a cylindrical coordinate system; completing independent variable transformation from a z coordinate to an x coordinateby using the simplified control equation; implementing Chebyshev forward transformation on the simplified control equation, and mapping a physical space to a spectral space to form a discretized linear equation set in the spectral space; solving the discretized linear equation set in the spectral space to obtain a solution in the spectral space; implementing Chebyshev inverse transformation on thesolution in the spectral space, and mapping the solution in the spectral space back to the physical space; completing independent variable inverse transformation from an x coordinate to a z coordinate to obtain u (r, z), and solving a sound pressure field p; calculating propagation losses. The method is suitable for obtaining higher calculation precision under the condition that few discrete gridpoints are used, the calculation performance of a hardware platform can be brought into full play, and the speed of numerical simulation is remarkably increased.

Description

technical field [0001] The invention relates to underwater acoustic propagation technology, in particular to an underwater sound field numerical simulation method, system and medium based on Chebyshev polynomial spectrum. Background technique [0002] Sound waves are the main carrier of underwater long-distance transmission of information. Other means of communication that are widely used in the fields of ground, air, and space often cannot be effectively used underwater. For example, electromagnetic waves are rapidly absorbed and attenuated in water, and long-distance transmission cannot be achieved. It is very important and necessary to fully understand and correctly grasp the law of sound wave propagation under water. Taking the ocean as an example, the ocean, which covers about 71% of the earth's surface, is rich in energy, minerals, and biological resources. The protection and development of ocean resources cannot be separated from technologies such as detection and id...

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Problems solved by technology

[0007] However, in terms of numerical discretization methods, the finite difference method is currently the mainstream discretization method, which has the advantages of being easy to understand and simple to implement. Its main shortcomings include: first, the accuracy is not high, and the commonly used second-order For the accuracy requirements in areas with severe sound field changes, the use of higher-order differential schemes can make up for some gaps, but it brings disadvantages such as more complex calculation processes and the need to supplement additional boundary conditions. For smooth and sharply changing different areas, in order to improve the spatial resolution of the calculation, it is often necessary to reduce the grid spacing, which dramatically increases the storage and calculation overhead, and the sound field calculation speed cannot meet the application requirements

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