Simple conformal methods for finite-difference time-domain modeling of pressure-release surfaces

The finite-difference time-domain (FDTD) method provides a simple and accurate means of simulating a wide range of acoustic wave propagation problems. Unfortunately, the method has a voracious appetite for computational resources. For example, to accurately model scattering from a continuously varying pressure-release boundary, an FDTD grid is typically required that has a much finer discretization than is necessary to model propagation in a homogeneous space. Such a fine discretization can become prohibitive when considering large-scale problems. Two simple conformal techniques are presented for acoustic FDTD simulations of problems involving pressure-release boundaries. These techniques, which rely upon splitting velocity cells adjacent to the pressure-release boundary, significantly improve the accuracy of the results over those of the standard “staircase” representation of the boundary. These methods permit the use of a coarser FDTD grid than would otherwise be practical and yet add negligible computational cost. The improved accuracy of these split-cell techniques is shown for both a spherical scatterer and a spherical resonator.