Application of higher-order boundary element method to steady ship wave problem and time domain simulation of nonlinear gravity waves

A higher order boundary element method was developed to compute the wave-making resistance due to a steady ship motion in the calm water, and to simulate linear and steep nonlinear irregular waves in the time domain using a numerical wave tank.; The development of the higher order boundary element method involves the formulation of a method of accurately evaluating the higher order derivatives of the potential functions on an arbitrary boundary surface, and establishment of the discontinuous higher order boundary element method to deal with the edge problems.; Flow fields due to steady ship motion and nonlinear free surface waves are obtained by employing the three-dimensional Rankine source as the Green's function, corresponding boundary conditions, and higher order interpolation functions in the direct boundary integral equation.; Numerical computation of the steady ship wave was accomplished by applying the quasi-linear free surface boundary condition due to the double body, zero-wave radiation condition at the upstream region, and a cubic order variation of the potential functions and geometries. The effectiveness of the present numerical scheme is proven from the comparison of the wave-making resistance with the theory and experiment.; The numerical simulation of nonlinear gravity waves in the time domain was conducted by employing the modified Sommerfeld/Orlanski condition, an efficient numerical time integration scheme by a freeze assumption, and the newly developed higher order boundary element scheme as a Laplace solver. The excellence of the methodology is demonstrated by efficiently simulating linear irregular waves as well as steep nonlinear irregular interacting Stokes-like waves in a small three-dimensional numerical wave tank.