Finite-difference time-domain modeling for underwater acoustic scattering applications based on immersed boundary method

Abstract

This paper proposes a finite-difference time-domain (FDTD) method to solve underwater acoustic scattering problems by using the immersed boundary method (IBM). Spatial discretization and time integration are realized using high-order schemes on uniform/non-uniform Cartesian grids. The non-homogeneous radiation boundary condition is applied at the domain boundary at which the prescribed incoming acoustic wave is generated, and the scattered wave is absorbed simultaneously. The IBM based on ghost nodes is used to address the solid boundary condition. Benchmark acoustic problems, including acoustic radiation from a pulsating cylinder and a vibrating cylinder, acoustic scattering of a plane wave by a cylinder and a sphere, are considered to validate the numerical schemes and boundary treatments in two- and three-dimensions. Furthermore, the proposed method is applied to compute the acoustic scattering by a moving cylinder to demonstrate its potential in addressing a moving target. Finally, as an engineering application, the acoustic scattering from a two-dimensional submarine is determined. The acoustic fields and directivity patterns at various frequencies and incident angles are analyzed. The proposed FDTD-IBM model provides a computational platform for two- and three-dimensional acoustic scattering problems and can be applied to complex acoustic problems such as flow–sound interaction and moving boundary problems.