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