Hydrodynamic performance of an array of submerged rigid elliptic disks under wave scattering and radiation

Abstract This paper develops a mathematically rigorous framework for analyzing the scattering and radiation of water waves by an array of submerged elliptic disks in deep water, a significant generalization of the classical single-disk problem. The transition from one disk to multiple elliptic bodies introduces substantial analytical challenges, including strongly coupled hypersingular boundary-integral equations, nontrivial elliptic parametrizations and intricate multi-body interactions. These are tackled by an expansion–collocation (spectral) method based on associated Legendre polynomials, together with an analytic treatment of the hypersingular terms for elliptic domains, leading to a large but structured matrix system that captures full multi-body interaction. The resulting scheme is used to compute surface elevation, scattering characteristics, hydrodynamic forces, added mass and damping coefficients for various array configurations. The computations show how the interplay of geometry, spacing and submergence controls scattering behavior, hydrodynamic forces and radiation coefficients. The study thus provides both a mathematically robust methodology for treating wave interaction with arrays of non-circular bodies and physically relevant insight for the design of submerged wave-interacting structures such as wave energy devices and offshore components.