Enhanced Fourier modal analysis for water-wave diffractions induced by submerged periodic blocks with arbitrary cross sections

Analyzing wave diffraction by periodic structures is crucial in fluid dynamics, coastal engineering, and ocean engineering, with applications spanning wave–structure interactions, coastal protection, and wave energy utilization. Conventional numerical methods primarily utilize Green's functions formulated in cylindrical coordinate systems, which are restricted to two-dimensional geometries and are difficult to accommodate sharp corners. In this study, we present a novel numerical approach to investigate the multi-modal wave diffractions induced by three-dimensional periodic planar blocks within Cartesian coordinate systems. We first model wave diffraction for rectangular shapes using Fourier modal analysis and then reconstruct the boundary matching matrix as a classical Thomson–Haskell propagator, leveraging a block symmetry. To address computational challenges at high frequencies and for large block thicknesses, we implement cascaded transmission matrix algorithms, achieving a computational accuracy improvement of approximately 16 digits. Building on these rectangular block models, we extend the approach to periodic planar blocks with arbitrarily shaped cross sections by discretizing the shapes into finite rectangular elements. This robust numerical solver is valuable for the design of coastal breakwaters and ocean wave energy converter arrays.