Three Dimensional Time Domain Numerical Method For Large Amplitude Ship Motions

Large amplitude motions affect the safety and comfortability of ship,while the sever case can even cause overturning accident.Therefore,prediction of wave induced motions and sea loads with the best possible accuracy has very important significance in ship design.On the basis of linear theorem,weakly nonlinear theorem and body nonlinear theorem,the transient Green function method is adopted to solve the three-dimensional ship motion problems in time-domain.The main contents can be summarized as follows:As the fourth-order Ordinary Differential Equation(ODE)of transient Green function is a time-varying system,and it is always a bottleneck to design an effective algorithm for such systems.For a class of these systems,whose coefficient matrix is of time-varying polynomial,a modified precise integration method is proposed.Through introducing new variables and expanding dimensions,the system can be transformed into a time-invariant system,in which the transfer matrix can be computed for once and used forever with a precise integration method.Some numerical examples demonstrate the validity of the method proposed,which is used in the computation of time-domain Green function for infinite depth case,and the method attains higher precision and better stability than common methods.The numerical methods for solving linear unsteady radiation and difraction problems with forward speed effects are established in this paper.And the CPU capacity of 3-D time-domain program is analyzed briefly.The numerical simulations of Wigley hull moving in head regular waves and long crested irregular waves are carried out,and the hydrodynamic coefficients,wave forces and motion amplitudes agree well with the available results and experiment data.It is verified the accuracy and reliability of the numerical simulation program in time-domain.Furthermore,based on the weakly nonlinear method,the Froude-Krylov nonlinear model in time domain is established in this paper.In this formulation,the disturbance potential and the corresponding hydrodynamic force are computed as in the linear case,i.e.based on the mean wetted hull position.However,the incident wave forces and restoring forces are evaluated by integrating the total pressure including incident wave term and static term over the instantaneous wetted hull.The wetted hull here is taken as the surface formed by the exact position of the hull under the incident wave profile.In this work,two alternative schemes to determine the instantaneous wetted hull have been developed.Then the wave profile correction method is adopted to evaluate the pressure at the panel centers.The numerical simulations of nonlinear ship motion in waves are carried out,and the nonlinearities and speed effects on computational results are discussed then.At last,on the basis of body nonlinear theorem,the numerical calculation method in time domain is established in this paper.This study focuses on solving the hydrodynamic problems that large amplitude motion response induced by small amplitude incident waves.In this formulation,the perturbation potential is solved based on the wetted hull formed by instantaneous position of the hull under the mean water line.Therefore,a practical and efficient numerical scheme is introduced for re-panelization of the instantaneous wetted hull.At every instant of time,the hydrodynamic and motion equations are solved simultaneously by a dynamic body boundary condition.Numerical tests are carried out for submerged and floating bodies,respectively.The comparisons of linear and nonlinear computations show that the body nonlinearity has considerable influence on results.