Hydraulic Design Optimization of a Multi-Stage Overtopping Wave Energy Converter Using WCSPH Methodology Under Site-Specific Wave Conditions

In multi-level overtopping wave energy converters (OWEC), the inlet slot governs overtopping losses and the distribution of inflow among reservoirs, making it a critical design feature for maximizing hydraulic efficiency. This study defines the relative slot width as λ (=w/Lslop) and investigates its influence on the performance of an SSG-based multi-level OWEC using DualSPHysics, an open-source weakly compressible smoothed particle hydrodynamics (WCSPH) solver, in a two-dimensional recirculating numerical wave tank under regular-wave conditions. Hydraulic efficiency is evaluated as the ratio of the overtopping-stored potential-energy flux to the incident wave energy flux per unit width. The results show a nonlinear dependence of reservoir-level contributions on λ, and an intermediate λ provides a balanced contribution across upper, middle, and lower reservoirs, yielding the maximum overall efficiency. To extend the analysis beyond a single design wave, a global-state performance map in the period–height space is constructed and combined with the target-sea spectral characteristics, indicating that the optimal geometry maintains relatively robust efficiency in the dominant spectral band while revealing efficiency limitations associated with insufficient overtopping at small waves and saturation at large waves. The proposed approach provides quantitative guidance for slot design and site-relevant performance screening of multi-level OWEC.