Hydrodynamic interactions between multi-scale ships pose significant challenges due to the substantial scale disparity, which drastically elevates computational complexity and typically induces numerical instability in conventional methods. To address this, this paper develops a one-way coupling method based on frequency-domain potential flow theory, achieved by decoupling the hydrodynamic solutions of the two ships. Specifically, the background flow field (including radiation and diffraction components) induced by the larger ship is first solved, after which the hydrodynamic forces and motions of the smaller ship are evaluated within this field. The theoretical framework is formulated, a dedicated numerical code is developed, and its computational accuracy and efficiency are systematically validated. Numerical results demonstrate that for a scale ratio of 1:5, the proposed one-way coupling method achieves accuracy comparable to the two-way coupling method, while offering approximately double the computational efficiency. Notably, as the scale disparity increases to 1:10, the two-way coupling method suffers from numerical instability attributed to the significantly elevated condition number of the coefficient matrix, whereas the present one-way coupling method maintains stability and accuracy by decoupling the boundary integral equations of the two ships. Consequently, this study establishes the one-way coupling strategy as a robust and efficient alternative that overcomes the stability limitations of conventional methods, particularly for simulating interactions between multi-scale or tandem-arranged ships with forward speed.
Fan et al. (Fri,) studied this question.