A fast integration method for translating-pulsating source Green’s function in Bessho form

The singularities and oscillatory performance of translating-pulsating source Green’s function in Bessho form were analyzed. Relative numerical integration methods such as Gaussian quadrature rule, variable substitution method (VSM), and steepest descent integration method (SDIM) were used to evaluate this type of Green’s function. For SDIM, the complex domain was restricted only on the θ-plane. Meanwhile, the integral along the real axis was computed by use of the VSM to avoid the complication of a numerical search of the steepest descent line. Furthermore, the steepest descent line was represented by the B-spline function. Based on this representation, a new self-compatible integration method corresponding to parametric t was established. The numerical method was validated through comparison with other existing results, and was shown to be efficient and reliable in the calculation of the velocity potentials for the 3D seakeeping and hydrodynamic performance of floating structures moving in waves.