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

D'ELÍA, J.; BATTAGLIA, L.; STORTI, M. A.

MATEMATICA APLICADA E COMPUTACIONAL

SOC BRASILEIRA MATEMATICA APLICADA & COMPUTACIONAL

Año: 2011 vol. 30 p. 267 - 287

0101-8205

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 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 singular one. The proposed computation is employed in a low order panel method with 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.