A semi-analytical computation of the Kelvin kernel for potential flows with a free surface

a semi-analytical computation of the three dimensional green function for seakeeping flow problems is proposed. a potential flow model is assumed with an harmonic dependence on time and a linearized free surface boundary condition. the multiplicative green function is expressed as the product of a time part and a spatial one. 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 singular one. the proposed computation is employed in a low order panel method with flat triangular elements. as a numerical example, an oscillating floating unit hemisphere in heave and surge modes is considered, where analytical and semi-analytical solutions are taken as a reference.