FINITE DIFFERENCE METHOD FOR 2-D AND 3-D NONLINEAR FREE SURFACE WAVE PROBLEMS

A finite difference method is developed for the numerical modelling of the 2-D and 3-Dunsteady potential flow generated by transient disturbances on the free surface, on which the non-linear boundary conditions are fully satisfied. The unknown function is computed with an iterationscheme processing in a transformed time-invariant space. After the velocity is calculated, the locationof the free surface is renewed and so is the value of velocity on it. The boundary-value problem of thegoverning equation is then solved at the next time step. The present method incorporates the FFT.Consequently, a tri-diagonal equation system is obtained which could be readily solved. The feasibilityof this method has been demonstrated by 2-D and 3-D examples corresponding to different initialdisturbances.