A practical computational method based on the Neumann−Kelvin (NK) theory is proposed for the rapid calculation of wave-making resistance.

The boundary integral equation is discretized and solved using the Kelvin source Green's function. Numerical computations of wave-making resistance, sinkage, trim, and free-surface elevation are performed for the Wigley and S60 hull forms using a self-developed Fortran program. The results are compared with experimental data and other numerical results to analyze the effects of waterline integration and different computational approaches. Furthermore, taking the KCS container ship as an example, this study examines the differences in grid sensitivity and computational accuracy between the pressure integration method and the wave pattern analysis method when calculating the wave-making resistance of hulls with complex geometries.

The results show that omitting the waterline integration term in the NK theory yields reasonably accurate predictions, with significantly improved applicability at medium to high speeds. The wave patterns along the hull sides exhibit low sensitivity to grid density, enabling convergence with relatively coarse grids. For hulls with complex geometries, the wave pattern analysis method ensures computational accuracy while significantly reducing grid requirements and computational costs.

This study offers a simplified and efficient practical tool for ship resistance evaluation and hull form optimization.

To simulate the complex nonlinear interactions between the free surface and instantaneous wetted hull surface during ship navigation, an automatic mesh generation method is proposed.

The method takes a whole-hull triangular mesh file as the input and automatically generates meshes for the instantaneously transforming free surface and wetted hull surface. It is able to handle arbitrary hullforms with complex bow and stern geometries while exhibiting strong robustness. Simulations of waves generated by a KCS hull at various speeds are then conducted using the proposed method.

The predicted ship-side wave profiles, wave patterns around the hull, and wave-making resistance show good agreement with the experimental results. Moreover, at higher speeds, the simulated wave surface at the KCS stern consistently stays below the transom, exhibiting a dry transom characteristic.

The results demonstrate that the proposed method can accurately model nonlinear ship waves and has the potential to simulate the flow fields around transom-stern ships.