Verification of a new radiation condition for two ships advancing in waves

•A new radiation condition was applied to ship-to-ship with forward speed problem.•More complementary equations were added to explain the complicated wave systems.•The proposed radiation condition was validated by model tests.•The wave pattern predicted by the proposed method is more reasonable.•The method is applicable for very low forward speed problem.

3-D Rankine source method is used to investigate the hydrodynamic interactions between two ships arranged side by side with forward speed. The radiation condition is satisfied by using a modified Sommerfeld radiation condition which takes into account the Doppler shift of the scattered waves. This new radiation condition is applicable to a wide range of forward speeds, including very low forward speed problem where the parameter τ (τ = uω/g) is smaller than 0.25. The numerical solution is evaluated by applying the present method to two pairs of models and compared with experimental data and Green function method. Through the comparison study, we verify the new radiation condition and examine the wave patterns for a full range of forward speeds. Discussions are highlighted on the effect of the radiation conditions.