A finite-difference time-domain solution to scattering from a rough pressure-release surface

Abstract

The finite-difference time-domain (FDTD) method is a numerical technique that makes no explicit physical approximations to the underlying problem. The quality of a FDTD-based solution typically is determined by the discretization of the computational domain—the smaller the spacing, the more accurate the solution. Unfortunately, for large computational domains, i.e., ones spanning many wavelengths, the small spatial step size needed to obtain a high-fidelity solution may lead to a prohibitively large number of unknowns. Here it is shown how the FDTD method can be used to model accurately scattering from pressure-release surfaces above a homogeneous water column. To keep the computational cost manageable, a number of enhancements to the standard FDTD algorithm are employed. These enhancements include correcting for numerical dispersion along the specular direction of the incident insonification, using locally conformal cells at the pressure-release boundary, and propagating the field through the homogeneous water column via an analytic method. The accuracy of the FDTD approach is demonstrated by comparison with an integral equation-based reference solution to the same rough surface scattering problem [Thorsos, Proceedings of the Reverberation and Scattering Workshop, pp. 3.2–3.20 (1994) Naval Research Laboratory Book Contribution NRL/BE/7181-96-001].