Application of a Spectral Method to Simulate Quasi-Three-Dimensional Underwater Acoustic Fields

The solution and synthesis of quasi-three-dimensional sound fields have always been core issues in computational ocean acoustics. Traditionally, finite difference algorithms have been employed to solve these problems. In this paper, a novel numerical algorithm based on the spectral method is devised. The quasi-three-dimensional problem is transformed into a problem resembling a two-dimensional line source using an integral transformation strategy. Then, a stair-step approximation is adopted to address the range dependence of the two-dimensional problem; because this approximation is essentially a discretization, the range-dependent two-dimensional problem is further simplified into a one-dimensional problem. Finally, we apply the Chebyshev--Tau spectral method to accurately solve the one-dimensional problem. We present the corresponding numerical program for the proposed algorithm and describe some representative numerical examples. The simulation results ultimately verify the reliability and capability of the proposed algorithm.Comment: 43 pages, 20 figures. arXiv admin note: text overlap with arXiv:2112.1360

Two Chebyshev Spectral Methods for Solving Normal Modes in Atmospheric Acoustics

The normal mode model is important in computational atmospheric acoustics. It is often used to compute the atmospheric acoustic field under a time-independent single-frequency sound source. Its solution consists of a set of discrete modes radiating into the upper atmosphere, usually related to the continuous spectrum. In this article, we present two spectral methods, the Chebyshev-Tau and Chebyshev-Collocation methods, to solve for the atmospheric acoustic normal modes, and corresponding programs are developed. The two spectral methods successfully transform the problem of searching for the modal wavenumbers in the complex plane into a simple dense matrix eigenvalue problem by projecting the governing equation onto a set of orthogonal bases, which can be easily solved through linear algebra methods. After the eigenvalues and eigenvectors are obtained, the horizontal wavenumbers and their corresponding modes can be obtained with simple processing. Numerical experiments were examined for both downwind and upwind conditions to verify the effectiveness of the methods. The running time data indicated that both spectral methods proposed in this article are faster than the Legendre-Galerkin spectral method proposed previously