To analyze force of fluid on a rigid object near free surface,a mathematical model with free surface effect is developed based on potential flow theory.It is calculated with boundary element method.Nonlinear kinematic and dynamic boundary conditions are taken into consideration.With control equation and boundary conditions,piercing cylinder through free surface and phenomena of spike are simulated.A comparison between numerical and experimental results shows that the method is appropriate.Pressure on moving objects,transform of free surface,resultant hydrodynamic force and velocity of flow field are analyzed in detail.It shows that the nonlinear method with free surface effect predicts precisely force on moving objects in vicinity of free surface.

We introduce Gaussian quadrature into calculation of frequency-domain Green functions and their partial derivatives.Compared with referenced methods the method proposed simplifies compution,reduces zoning and improves computing efficiency with sufficient accuracy.