Objectives With the formal release of the interim guidelines on the second generation intact stability criteria (SGISc) by the international maritime organization (IMO) in 2020, the research focus has shifted from vulnerability criteria to direct stability assessment (DSA) and operational guidance. Surf-riding, a typical stability failure mode induced by the coupling of ship maneuverability and seakeeping performance, often occurs in following and stern-quartering waves, and may further trigger broaching, leading to loss of course-keeping, stability failure, and even capsizing. To address the urgent demand for direct assessment of surf-riding instability and support the improvement of DSA methods under the SGISc framework, this study aims to establish an effective numerical prediction method for surf-riding motion and conduct in-depth analysis of its occurrence mechanism and motion characteristics.

Methods A computational fluid dynamics (CFD) approach based on the Reynolds-averaged Navier-Stokes (RANS) equations was adopted, integrated with overset grid technology to accurately capture the six-degree-of-freedom (6-DOF) motion of the self-propelled ship model and propeller body-force model to balance computational accuracy and efficiency. The numerical method incorporated volume of fluid (VOF) method with high-resolution interface capturing (HRIC) for free surface treatment, SST k-ω turbulence model for turbulence closure, and wave forcing method for wave generation and absorption. Taking the ONR tumblehome (ONRT) hull, a standard ship model from the Tokyo 2015 CFD Workshop on Ship Hydrodynamics, as the research object, numerical simulations of surf-riding phenomena in regular following and stern-quartering waves at high forward speeds (Froude number Fr = 0.30, 0.35, 0.40, 0.45) were carried out. The computational conditions covered wave length-ship length ratios (λ/L_pp) of 1.25 and 1.50, wave steepness of 0.05, and wave headings of 5° and 15°. The simulation results were systematically compared with published experimental data from the University of Osaka to validate the proposed method.

Results The calm water self-propulsion simulation results showed that the mean prediction error of propeller rotational speed across different forward speeds was 10.11%, with the minimum error of 8.06% at Fr = 0.35, and the mean error of total resistance was only 3.13%, indicating good agreement with experimental values. In wave conditions, the numerical simulation successfully captured the transition between periodic motion and surf-riding state: when Fr = 0.30, the ship speed was lower than the wave speed, failing to be captured by waves and maintaining periodic motion; when Fr ≥ 0.35, the ship entered a stable surf-riding state with ship speed matching the wave celerity. The wave conditions triggering surf-riding were consistent with experimental results, and the calculated maximum roll amplitudes showed the same variation trend as the measurements. However, under the condition of heading 15°, Fr = 0.35, and λ/L_pp = 1.25, the experiment observed broaching while the simulation showed surf-riding, which might be attributed to the sensitivity of broaching (a strongly nonlinear random motion) to initial ship-wave relative positions.

Conclusions The study confirms that the propeller body-force based CFD method can effectively predict surf-riding motion at high speeds with higher computational efficiency compared to the discrete propeller model, providing a reliable tool for direct stability assessment of surf-riding. For the ONR tumblehome hull, under the same wave conditions, the heave displacement in surf-riding equilibrium increases with the increase of ship speed, while the pitch and roll angles decrease, accompanied by varying degrees of bow burying and green water due to its wave-piercing bow design. The proposed numerical method and mechanism analysis can provide a technical basis for future surf-riding simulations in irregular waves, and the unpredicted broaching in specific conditions suggests that subsequent studies should focus on the influence of initial conditions to improve the prediction accuracy of nonlinear instability modes..