Locally conformal method for acoustic finite-difference time-domain modeling of rigid surfaces

The finite-difference time-domain method is a simple but powerful numerical method for simulating full-wave acoustic propagation and scattering. However, the method can demand a large amount of computational resources. Traditionally, continuously curved boundaries are represented in a stair-step fashion and thus accurately modeling scattering from a boundary will require a finer discretization than would otherwise be necessary for modeling propagation in a homogeneous medium. However, a fine discretization might not be practical due to limited computational resources. A locally conformal technique is presented here for modeling acoustic scattering from continuously curved rigid boundaries. This technique is low cost, simple to implement, and gives better results for the same grid discretization than the traditional stair-step representation. These improvements can be traded for a coarser discretization which reduces the computational burden. The improved accuracy of this technique is demonstrated for a spherical scatterer.