Green Function Solutions for the Transient Motion of Water Sections

A time-domain boundary element method based on a Green function solution is derived for two-dimensional motions in the presence of a free liquid surface. Particular attention is given to the numerical evaluation of the required Green functions with regard to accuracy and speed of solution by choice of a computational algorithm appropriate to the domain of particular computations. The method is validated with reference to analytic solutions for submerged and floating cylinders in steady, transient and periodic motion. The intended application of the method is in the computation of wave response of slender ships at high Froude number by a fixed frame strip theory where the Green function obviates the necessity to panel the free surface with elements.