When numerically analyzing acoustic scattering at a pressure-release rough surface, the conventional pseudospectral time domain (PSTD) method using Fourier transform requires rigorous stability conditions in order to solve the spatial derivative in the wave equation on the irregular boundaries between the two media due to the Gibbs phenomenon and short wavelength in air. To eliminate such disadvantages, a new algorithm is proposed based on the Fourier PSTD method utilizing a surface boundary transformation and an image method. Irregular surface boundaries are flattened by transformation and then an image method is applied to the half-space domain. The efficiency and accuracy of the proposed PSTD method are better than the conventional Fourier PSTD method. Numerical results are presented for a sloped and a sinusoidal pressure-release surface.

A pseudospectral time-domain (PSTD) method using a surface flattening transformation and image method is applied to a randomly rough pressure-release surface scattering problem. Above, the PSTD method efficiently avoids the Gibbs phenomenon appearing in the conventional PSTD method when treating irregular boundaries with large impedance contrast. The pressure-release surface is generated by Pierson–Moskowitz spectrum and Monte Carlo method is used to calculate the statistical properties of the rough surface. The Monte Carlo results for elemental scattering area will be investigated by comparing with Chapman–Harris formula.