Analytical Formulations in the Domain Decomposition Method using Cylindrical Control Surface

Abstract

The seakeeping problem is very important for marine structures, but present boundary element methods have still unresolved difficulties. In this work, the Green function method (Green function satisfying the linear boundary condition at free surface) is combined with the Rankine panel method so that two methods keep their advantages and brings important benefits. The fluid domain is divided into two subdomains by a control surface of cylindrical form. In the interior one the ship is arbitrary, the Rankine source method is then applied. In the exterior one the shape of the control surface is analytically known while the velocity potential and its normal derivative are expressed by expansions of orthogonal functions. Across the control surface two additional conditions must be satisfied: both the velocity potential and its normal derivative are to be continuous. In order to improve the computational accuracy, velocity potential is decomposed by using the Fourier series in polar direction and Laguerre function in vertical direction on the cylindrical control surface. The matrix elements of boundary integral equations consist of analytical integrations in wavenumber. Furthermore, the numerical results of the integrals are presented for seakeeping problems.