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

D'ELIA, JORGE; BATTAGLIA, LAURA; STORTI, MARIO

COMPUTATIONAL AND APPLIED MATHEMATICS

Springer, SP Birkhäuser Verlag Basel

Lugar: DOI:10.1007/s40314-013-0043-5; Año: 2010 vol. 30 p. 267 - 287

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.