Abstract
The finite element method is a popular numerical method in engineering applications. However, there is not enough research about the finite element method in underwater sound propagation. The finite element method can achieve high accuracy and great universality. We aim to develop a three-dimensional finite element model focusing on underwater sound propagation. As the foundation of this research, we put forward a finite element model in the Cartesian coordinate system for a sound field in a two-dimensional environment. We firstly introduce the details of the implementation of the finite element model, as well as different methods to deal with boundary conditions and a comparison of these methods. Then, we use four-node quadrilateral elements to discretize the physical domain, and apply the perfectly matched layer approach to deal with the infinite region. After that, we apply the model to underwater sound propagation problems including the wedge-shaped waveguide benchmark problem and the problem where the bathymetry consists of a sloping region and a flat region. The results by the presented finite element model are in excellent agreement with analytical and benchmark numerical solutions, implying that the presented finite element model is able to solve complex two-dimensional underwater sound propagation problems accurately. In the end, we compare the finite element model with the popular normal mode model KRAKEN by calculating sound fields in Pekeris waveguides, and find that the finite element model has better universality than KRAKEN.
Highlights
There are a variety of methods for calculating the underwater sound fields, such as the ray method, the normal mode method, and the parabolic equation method
Finite element methods for time–harmonic acoustics governed by the Helmholtz equation have been an active research area over the past 50 years
Initial applications of finite element methods for time–harmonic acoustics focused on interior problems with complex geometries including direct and modal coupling of structural acoustic systems for forced vibration analysis, frequency response of acoustic enclosures, and waveguides [2,3,4]
Summary
There are a variety of methods for calculating the underwater sound fields, such as the ray method, the normal mode method, and the parabolic equation method. The finite element method is used by only a few researchers to solve underwater sound propagation problems. Finite element methods for time–harmonic acoustics governed by the Helmholtz equation have been an active research area over the past 50 years. Initial applications of finite element methods for time–harmonic acoustics focused on interior problems with complex geometries including direct and modal coupling of structural acoustic systems for forced vibration analysis, frequency response of acoustic enclosures, and waveguides [2,3,4]. Tremendous progress has been made; for example, extending the finite element method to exterior problems in unbounded domains and higher frequency regimes, which incorporates knowledge of wave behavior into the algorithm, combined with parallel sparse interactive and domain decomposition solvers
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