An efficient finite-difference approach for optimizing sloshing dampers to minimize tank waves excited by ship motions

Mitigating sloshing in shipboard tanks, such as swimming pools, is critical for passenger safety and comfort, as excessive waves induced by ship roll motions pose significant risks. Traditional experimental and numerical methods for evaluating mitigation strategies are often impractical due to high cost and computational demand. To address this challenge, this study proposes a computationally efficient linear finite-difference method (FDM) to optimize active sloshing dampers that minimize tank waves excited by ship motions. Active suppression is achieved using piston-type actuators installed at the ends of rectangular tanks subjected to periodic excitation. The developed approach predicts wave behavior and determines optimal actuator amplitudes, enabling parametric studies of tank geometry, fill level, and excitation frequency. Results obtained from the efficient approach are validated against high-fidelity simulations based on the Reynolds-averaged Navier–Stokes (RANS) equations, demonstrating strong agreement. The comparisons further delineate the practical validity range, with strongest agreement observed for long waves, while deviations increase as the wavelength decreases and under excitation conditions close to resonance, where nonlinear effects become more pronounced. The findings confirm that piston-type actuators effectively mitigate wave amplitudes across a broad range of conditions, and a functional relationship between the optimal actuator amplitude and key tank parameters is established. Overall, the proposed method provides a fast and reliable predictive tool, offering significant advantages for rapid evaluation and early-stage design of active wave mitigation systems in shipboard applications.