A sixth-order finite difference model coupled with the matched interface and boundary method for underwater acoustic propagation simulations

Abstract

To improve the accuracy of seabed processing in finite difference (FD) models for ocean acoustic field simulations, a nominal fifth-order matched interface and boundary (MIB) method is developed, which can automatically determine the highest achievable order of accuracy near boundaries or complex seabed interfaces. Since the MIB method can separate the discretization of partial differential equations from the implementation of interface conditions, a sixth-order FD scheme is also developed to discretize the acoustic Helmholtz equation coupled with the fifth-order MIB method. This FD scheme is applied to each grid line segment whose end nodes are either the physical boundary nodes or the MIB ghost nodes, and the FD scheme near the MIB ghost nodes is designed to be consistent with that at the boundary nodes. Furthermore, the accuracy of the present FD model has been numerically verified using two- and three-dimensional acoustic benchmarks, including a newly designed C-shaped atoll acoustic propagation case. Compared with the fourth-order FD model using the smoothing approximation method to handle the seabed, which requires a PPW (points per wavelength) of 30∼60 for the accurate computation of a general non-flat ocean acoustic field, the proposed sixth-order FD model coupled with the MIB method requires only a PPW of 8 with the comparable solution accuracy, leading to a significant improvement in the computational efficiency of three-dimensional ocean acoustic field simulations.