Prediction of Added Resistance in Waves Using a Frequency-Domain Rankine Source Method: Middle-Field Formulation and Low-Speed Validation

A three-dimensional frequency-domain ship-motion solver based on the Rankine source method is extended to predict added resistance in waves. Although middle-field formulations have been used mainly in time-domain Rankine panel methods, a middle-field evaluation is implemented here within a frequency-domain Rankine source framework and its validity is examined, including low-speed conditions where the enforcement of radiation conditions is challenging. To enhance robustness at low forward speeds, a hybrid radiation technique is incorporated. Convergence studies are carried out for the free-surface and radiation-boundary discretization, as well as for the control-surface resolution and the clearance distance, and practical numerical settings for added-resistance computations are established. The approach is first verified for Wigley III hulls by comparing motion RAOs and added resistance with published experimental and numerical results. It is then validated for the blunt KVLCC2 hull at the design speed and at low speeds (0 and 4 knots) against published measurements and calculations. Further validations are conducted for additional hull forms (Wigley I, KCS, S-175, and Series 60). The results indicate that the proposed frequency-domain Rankine source method with middle-field evaluation and hybrid radiation yields consistent predictions of motion responses and added resistance over a range of speeds and hull forms, while retaining computational efficiency.