Computational & Applied Mathematics
versão On-line ISSN 1807-0302
D'ELIA, Jorge; BATTAGLIA, Laura e STORTI, Mario. A semi-analytical computation of the Kelvin kernel for potential flows with a free surface. Comput. Appl. Math. [online]. 2011, vol.30, n.2, pp. 267-287. ISSN 1807-0302. http://dx.doi.org/10.1590/S1807-03022011000200002.
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.
Palavras-chave : green function; boundary integral equation; three dimensional potential flow; free surface; computational techniques.