Semi-Analytical Formulation of the Second-Order Wave Diffraction by a Truncated-Compound Surface-Piercing Cylinder

The second-order diffraction potential around a truncated-compound cylinder is considered. The solution method is based on a semi-analytical formulation of the double-frequency diffraction potentials and results in two different Sturm-Liouville problems which are treated separately in the ring-shaped fluid regions defined by the geometry of the structure. Different Green functions are constructed for the fluid fields that extend up to the free surface. The calculation of integrals of the pressure distribution on the free surface is carried out using an appropriate Gauss-Legendre numerical technique.