An optimized, parameter-free PML-FEM for wave scattering problems in the ocean and coastal environment

Abstract

Water-wave propagation in nearshore regions and hydroacoustic scattering problems, in the presence of structures, are fundamental to ocean and coastal engineering. Efficient modelling of these phenomena can be achieved using the Helmholtz equation with spatially varying coefficients to which mild-slope models are reducible. Despite the relatively simple forms of these models, geometric and medium inhomogeneities and inclusions, yield complex wavefield solutions that can only be numerically approximated. However, the numerical treatment of such problems in infinite domains requires the truncation of the computational region. In this work, an optimal, parameter-free Perfectly Matched Layer (PML) model is implemented in a Finite Element scheme. The fundamental similarities between the governing equations for steady-state water wave and hydroacoustic scattering problems allow for a joint analysis of the proposed PML-FEM solution strategy. Excellent convergence characteristics are verified through comparisons against benchmark solutions. Water-wave propagation solutions for an uneven seabed featuring an elliptic shoal are compared with available experimental data. Also, wave diffraction by vertical cylinders in regions of variable bathymetry, and scattering by an elliptically shaped body in the ocean-acoustic waveguide, are studied. The proposed numerical scheme is found to be an efficient means to tackle challenging wave-seabed-body interaction problems in large spatial domains.