Implicit expressions of static and incident wave pressures over the instantaneous wetted surface of ships

To predict a ship's behaviour, adopting either a partial or comprehensive non-linear hydrodynamic method, requires accurate information of incident wave and static pressure on any location over the instantaneous wetted hull surface. In this study an implicit formula to evaluate the non-linear hydrostatic and incident wave dynamic pressures acting on a ship travelling in linear or second-order deep water incident waves is deduced based on a wave mapping method. The accuracy and efficiency of the numerical scheme of study employing this formula is verified and validated through comparisons with a simple extrapolation (or stretching) approach, Wheeler stretching methods, and with a fifth-order Stokes' wave theory, which is assumed to embody a more complete solution. More accurate predictions of the dynamic pressure are achieved from the proposed second-order wave mapping method. However, as a practical approach, the presented second-order wave Wheeler stretching method can be considered as a reasonable approximation to the proposed wave mapping method.