A Semi-Analytical Computation of the Kelvin Kernel for Potential Flows with a Free Surface

Abstract

A semi-analytical computation of the three dimen- sional Green function for seakeeping flow problems is proposed. A potential flow model is assumed with an harmonic depen- dence in time and a linearized free-surface boundary condition. The multiplicative Green function is expressed as the product of a time and a spatial parts. The spatial part is known as the Kelvin kernel, which is the sum of two Rankine sources and a wave-like kernel, being the last one written using the Haskind- Havelock representation. Numerical efficiency is improved by an analytical integration of the two Rankine kernels and the use of a singularity subtractive technique for the Haskind-Havelock integral, where a globally adaptive quadrature is performed for the regular part and an analytic integration is used for the sin- gular one. The proposed computation is employed in a low or- der panel method with flat triangular elements. As a numerical example, an oscillating fl oating unit hemisphere in heave and surge modes is considered, where analytical and semi-analytical solutions are taken as a reference.