An FDTD Method for Analysis of Scattering from Rough Fluid–Fluid Interfaces

A finite-difference time-domain (FDTD) method for scattering by one-dimensional, rough fluid–fluid interfaces is presented. Modifications to the traditional FDTD algorithm are implemented which yield greater accuracy at lower computational cost. These modifications include use of a conformal technique, in which the grid conforms locally to the interface, and a correction for the numerical dispersion inherent to the FDTD algorithm. Numerical results are presented for fluid–fluid cases modeling water–sediment interfaces. Two different roughness spectra, the single-scale Gaussian roughness spectrum and a multiscale modified power-law spectrum, are used. The Gaussian results are calculated as a function of the dimensionless parameters and , where is the wavenumber in water, is the rms surface height, and is the surface correlation length. For the modified power-law spectrum, statistical parameters consistent with an insonification frequency of 7.5 kHz are used. Results are compared with those obtained using an integral equation technique both for scattering from single-surface realizations and for Monte Carlo averages of scattering from an ensemble of surface realizations. Scattering strengths are calculated as a function of scattering angle for an incident angle of ( grazing). The results agree well over all scattering angles for the cases examined.