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.