Numerical Integration of Green Source Function with Free Water Surface and Zero Advancing Speed

A numerical integration method on 3D Green source function with free water surface and zero advancing speed is proposed. Zero order Laplace transformation makes the Green source function easily to be truncated. Various integration methods are used according to the characteristics of the function in different areas. Spline fit and adaptive program are used to integrate the oscillating functions. The numerical solution for an oscill ating hemisphere on the free surface with zero advancing speed gives a satisfactory result.