A Novel Finite Difference Scheme for Normal Mode Models in Underwater Acoustics

Author:

Liu Wei1ORCID,Xu Guojun1,Cheng Xinghua1,Wang Yongxian1ORCID

Affiliation:

1. College of Meteorology and Oceanography, National University of Defense Technology, Changsha 410073, China

Abstract

Normal mode models are commonly used to simulate sound propagation problems in horizontally stratified oceanic environments. Although several normal mode models have been developed, the fundamental techniques for accurately and efficiently solving the modal equation are still under development. Since the standard three-point central finite difference scheme (SFD) for the modal equation has a relatively large numerical error, at least twenty sampling grid points per wavelength should be set in the depth direction. Herein, a novel finite difference scheme (NFD) is developed to further improve the accuracy of the mode solution, and the resulting linear system still has a tridiagonal structure similar to that of the SFD. To compare the performance of the NFD to that of the SFD, the NFD has been implemented in the open-source normal mode model KrakenC, and three acoustic propagation cases have been carried out, including the plane-wave reflection, the Pekeris waveguide, and the Munk waveguide. Test results show that the NFD presented in this paper is more accurate than the SFD, and can be used to reduce the number of grid points needed in the depth direction for solving the modal equation in normal mode models.

Funder

National Natural Science Foundation of China

National Key Research and Development Program of China

Aerospace Support Technology Fund of China

Publisher

MDPI AG

Subject

Ocean Engineering,Water Science and Technology,Civil and Structural Engineering

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