Objectives Since the early 21st century, driven by the integration of ship engineering and fluid mechanics, the research and development of large container ships and special vessel types have become key drivers of global trade, energy transportation, and port dredging. With the intelligent upgrading of canal networks, ship navigation efficiency has been significantly improved, while the requirements for navigation safety control have increased, necessitating more refined studies on hydrodynamic characteristics. Therefore, the research on various hydrodynamic coefficients is crucial, as they are directly related to the maneuvering performance of ships. Current research methods mainly include theoretical calculations, empirical formulas, model tests, and numerical simulations, among which model tests and numerical simulations are the two main approaches. Planar motion mechanism (PMM) tests provide core experimental data for studying the dynamic hydrodynamic characteristics of ships through six-degree-of-freedom motion simulations. Due to the high cost and long duration of model experiments, numerical simulation technology has emerged as a cost-effective and efficient tool for hydrodynamic coefficient research, thanks to turbulence model optimization and parallel computing.

Methods The naoe-FOAM-SJTU solver, developed on the open-source platform OpenFOAM, is capable of handling dynamic overlapping grids. This solver integrates a self-developed multi-body six-degree-of-freedom motion solver module, enabling full simulation of various working conditions in ship PMM tests and facilitating comprehensive dynamic coupling analysis of fluid-structure interactions. For grid processing, the Suggar++ overlapping grid interpolation program is employed to generate domain connectivity information (DCI), ensuring accurate data transmission and stable coupling of flow field data between overlapping grids. In this study, the dynamic overlapping grid method is used in conjunction with the unsteady Reynolds-averaged Navier−Stokes (RANS) equations and SST k−ω turbulence model for numerical simulation. The SST k−ω model effectively combines the high accuracy of the k−ω model in the near-wall region with the robustness of the k−ε model in the far-field flow by closing the RANS equations. By introducing a mixing function and constraining the turbulent eddy viscosity, the model significantly improves the prediction accuracy of complex flows, especially separated flows. Based on the aforementioned numerical methods, a systematic hydrodynamic numerical simulation and analysis of the pure sway motion of the KVLCC1 ship model were carried out in both deep and shallow water environments with different water depth-to-draft ratios.

Results  Comparisons with experimental results show that the errors in sway force amplitude, yaw moment amplitude, and phase angle relative to the experimental values are mostly around 5%, verifying the feasibility of using the overlapping grid method for ship hydrodynamic calculations. This result further confirms that the selected calculation model can accurately reflect actual conditions, ensuring the effectiveness and credibility of numerical simulations in engineering applications. In both deep and shallow waters, the hydrodynamic coefficients in shallow water are significantly larger than those in deep water, which is closely related to the shallow water effect. This effect can lead to deteriorated maneuverability of ships in shallow water, especially during large-angle steering, where the maneuvering performance may be seriously affected. Additionally, the sway force amplitude and yaw moment amplitude are found to have a linear relationship with the dimensionless sway velocity amplitude v′. The shallow water effect significantly increases the flow velocity on both sides of the hull and the hull bottom. In areas with increased flow velocity gradients, the regions with higher flow velocity are mainly concentrated at the bow and stern in deep water, while they extend across the entire hull bottom in shallow water. In deep water, the velocity distribution behind the stern is more stable compared to that in shallow water. Regarding the wake, under deep water conditions, the wake is relatively stable, fully developed, and has a more regular shape than that under shallow water conditions. In shallow water, the low-velocity and low-pressure areas in the wake are more pronounced than those in deep water, which is caused by the insufficient development of the wake due to limited vertical space (z-direction). Furthermore, the forebody bilge vortex is less developed in shallow water due to restricted vertical space.

Conclusions This research provides valuable references for ship maneuverability analysis.