Fundamental Studies on Rankine Source Panel Method Fully Based on B-splines

Abstract

A free-surface boundary element method is presented for solving three-dimensional steady ship wave problem. The method approximates geometry and potential with a higher degree of continuity, compared to the other Rankine source methods. Global parametric B-spline tensor products define both the ship hull and the free-surface geometry. A skinning type algorithm based on de Boor procedure is developed to perform the surface fitting. B-splines of various degrees represent the unknown singularity distribution. The functions describing geometry and potential have independent structures and are connected on their parametric space. The influence coefficients are evaluated by adaptive Gauss quadratures after removing the singularity of Rankine source analytically. Kelvin's type free-surface condition and Kutta-like radiation condition ensure unique solutions. Involved derivatives of the potential are obtained directly, without using a difference scheme. Computations of the wave resistance for Wigley, Series 60, HTC container ship and SR221B tanker hull forms, approximated by a single patch, demonstrate the accuracy of the method.