Hydrodynamics-based analysis and physics-guided prediction of energy saving and emission reduction in longitudinal heterogeneous ship formations

• A physics guided multi-scale dynamic GNN is proposed for formation modeling. • A speed and spacing based physics gate enables multi-scale flow feature prediction. • Simulations show how ship type, number, speed and spacing shape formation resistance. • Analysis shows how bow flow and ship waves influence shear and pressure resistance. Resistance reduction through longitudinal ship formations provides an effective pathway for energy saving and emission reduction in maritime transportation. In this study, a hydrodynamic model of longitudinal heterogeneous ship formations is established based on STAR-CCM+, and the coupled effects of formation scale, sailing speed, inter-ship spacing, and ship-type differences on hydrodynamic characteristics are systematically analyzed. Numerical simulation results indicate that the bow flow velocity exhibits a positive correlation with viscous resistance, and that ship-generated waves exert a significant influence on the resistance characteristics of following ships at higher cruising speeds. On this basis, a physics-guided multi-scale dynamic graph neural network (PG-MDGNN) is proposed. By introducing a dynamic gating mechanism based on sailing speed and inter-ship spacing, together with a three-channel feature fusion strategy, the model enables multi-scale hydrodynamic modeling and prediction. Validation results demonstrate that the proposed model achieves favorable generalization performance in resistance prediction tasks for formations of varying scales, reducing the mean absolute error (MAE) by 17.7% compared with conventional methods. The findings of this study provide theoretical support for energy-efficient design and intelligent navigation decision-making in longitudinal heterogeneous ship formations.