Numerical modeling of nonlinear interactions between ships and surface gravity waves, part 1: Ship waves in calm water

This paper presents a pseudo-spectral model for nonlinear ship-surface wave interactions. The algorithm used in the model is a combination of spectral and boundary element methods: the boundary element method is used to translate physical quantities between the nonuniform ship surface and the regular grid of the spectral representation; the spectral method is used throughout the remainder of the fluid domain. All possible wave-wave interactions are included in the model (up to N-wave interactions for the truncation order N of the spectral expansions). This paper focuses on the mathematical theory and numerical method of the model and presents some numerical results for steady Kelvin waves in calm water. The nonlinear bow waves at high Froude numbers from the pseudo-spectral model are much closer to the experimental results than those from linear ship wave models. Our results demonstrate that the pseudo-spectral model is significantly faster than previous ship wave models: with the same resolution, the CPU time of the pseudo-spectral model is orders of magnitude less than those of previous models. Convergence speed of this model is ANLogN instead of BN2, where N is the number of unknown (note that the N for the traditional boundary element method may be significantly larger than the N for the pseudo-spectral method for the same quality solution). A and B are CPU time requirements in each time step for our model and others, respectively.