Three-dimensional finite element modeling of water wave propagation over canyon–cave composite seabed topography

This study presents an analytical and numerical framework for modeling three-dimensional water wave propagation over seabed topography with canyon–cave structures. A finite element formulation maintains full three-dimensional (3D) resolution without dimensional reduction, using implicit surface representations that capture features including overhangs and vertical walls. Numerical implementation employs linear tetrahedral and high-order spectral elements in a frequency-domain approach, analyzing wave periods (6–12 s) and incident angles (0°–90°). Reflection coefficients are calculated using a hybrid method combining regional amplitude comparison with standing wave ratio analysis. Results show scattering patterns with resonant behavior at specific wavelength-topography ratios. Reflection coefficients exhibit strong angular dependence, with transmission reaching 96.3% at optimal configurations. 3D flow field analysis reveals vertical wave potential deformation, pressure gradient variations, and velocity patterns demonstrating genuine 3D effects. The spectral element implementation provides a high-accuracy reference with reduced numerical dispersion. This framework offers an efficient tool for predicting wave transformation over complex bathymetry, applicable to offshore structure design and coastal hazard assessment. Computational efficiency (parameter studies under 7 s) suits iterative design and sensitivity analyses.