Objectives Following 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 resulting from the coupling of ship maneuverability and seakeeping performance, often occurs in following and stern-quartering waves. This phenomenon can trigger broaching, leading to a loss of course-keeping, stability failure, and even capsizing. To address the urgent need for direct assessment of surf-riding instability and support the enhancement of DSA methods under the SGISc framework, this study aims to develop an effective numerical prediction method for surf-riding motion and conduct a detailed 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 employed, integrated with overset grid technology to accurately capture the six-degree-of-freedom (6-DOF) motion of the self-propelled ship model. A propeller body-force model was used to balance computational accuracy and efficiency. The numerical method incorporated the volume of fluid (VOF) method with high-resolution interface capturing (HRIC) for free surface treatment, the SST k–ω turbulence model for turbulence closure, and a 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 were performed in regular following and stern-quartering waves at high forward speeds (Froude number Fr = 0.30, 0.35, 0.40, 0.45). The computational conditions included wave length-to-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 experimental data published by the University of Osaka to validate the proposed method.

Results The calm water self-propulsion simulation results indicated that the mean prediction error of the propeller rotational speed across different forward speeds was 10.11%, with the minimum error of 8.06% at Fr = 0.35. The mean error in total resistance was only 3.13%, showing good agreement with the experimental values. Under wave conditions, the numerical simulation successfully captured the transition between periodic motion and the surf-riding state. When Fr = 0.30, the ship speed was lower than the wave speed, preventing the ship from being captured by the waves, and the ship maintained periodic motion. When Fr ≥ 0.35, the ship entered a stable surf-riding state, with the ship speed matching the wave celerity. The wave conditions triggering surf-riding were consistent with experimental results, and the calculated maximum roll amplitudes exhibited the same 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. This discrepancy may be attributed to the sensitivity of broaching (a strongly nonlinear random motion) to the initial relative positions of the ship and waves.

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 the direct stability assessment of surf-riding. For the ONR tumblehome hull, under the same wave conditions, the heave displacement in the surf-riding equilibrium increases with the ship speed, while the pitch and roll angles decrease. This is accompanied by varying degrees of bow burying and green water due to this ship's wave-piercing bow design. The proposed numerical method and mechanism analysis can provide a technical foundation for future surf-riding simulations in irregular waves. The unpredicted broaching in specific conditions highlights the need for subsequent studies to focus on the influence of initial conditions to improve the prediction accuracy of nonlinear instability modes.