A Rapid Prediction Method for Gate-Rudder-Propeller Coupled Flow Fields with Multi-Reference-Frame Embedding and Physical Constraints

Objectives To address the high computational cost of multi-condition CFD simulations, the difficulty in representing the coupled rotating and stationary domains, and the poor predictability of near-wall loads in gate-rudder-propeller systems, a three-dimensional flow-field surrogate model is established to support rapid evaluation of ship propulsion systems.Methods A flow-field surrogate model integrating multi-reference-frame embedding, wall-distance awareness, wall-pressure supervision and progressive physical constraints is proposed. Block embedding represents the physical differences among the rotating domain, the stationary domain and the wall blocks; Fourier feature mapping enhances the representation of high-frequency wake structures behind the propeller; a KD-Tree wall-distance field together with a near-wall turbulent-viscosity envelope constrains the near-wall variables; wall-pressure auxiliary supervision constrains the surface loads of the propeller and the gate rudder; and the velocity-divergence residual is introduced progressively with a weight that increases smoothly with the training epoch.Results At J=0.55, which is not involved in training, the model reconstructs the propeller wake and the rudder-interference region. The NRMSE of the velocity magnitude is 4.22×10⁻², the R² of the pressure is 0.9936 and the R² of the turbulent viscosity is 0.9768. The relative errors of the propeller thrust and torque are 1.22% and 1.18%, and those of the gate rudder are 0.83% and 1.10%，respectively.Conclusions The accuracy of the model meets the requirements of rapid multi-condition evaluation and digital-twin modeling of ship propulsion systems.