Boundary Element Method for Wave Making Resistance of Ships

Modern computer technology enables simulations of free surface flows around a realistic ship hull. With the schemes of finite difference, finite element, and boundary element as the choice for the numerical algorithm, the boundary element method has been established as a popular approach for free surface wave computations owing to its efficiency, accuracy and flexibility. Potential flow based panel method are based on Green’s theorem which relates properties of flows within a domain to the domain boundary conditions. The pioneering work of Hess and Smith [1] change panel methods into the numerical calculation and simulation of potential flows for bodies of general shapes. There are normally two types of approaches towards the numerical solution of free surface flows. The first one is to adopt linearized free surface wave Green Function as the singularities distributed on the submerged hull surface and the uniform as the basis flow (Liapis [2], King [3], Beck et. al. [4], Korsmeyer [5] and Bingham [6]). While this method is elegant in enforcing free surface conditions and radiation conditions,it is difficult to extend the scheme to nonlinear solutions (Sclavounos [7]). The other approach, the Rankine Panel Method (RPM), was first introduced by Gadd [8] and Dawson [9], who employed the double body flow as the basis for linearization, chosen primarily trough physical intuition. The free surface is discretized into quadrilateral panels and covered by the Rankine sources and dipoles (Nakos [10], Raven [11], Jensen et. al. [12] and Kring [13]). In this paper, a kind of GFM for steady-state free-surface potential-flow problem is employed to develop a computer code which calculates wave making resistance and the wave pattern of ships. This method uses a distribution of sources located on the wetted surface of the ship to represent the velocity potential.